There are a lot of ideas out there already, a number of which could be quite interesting. Anyways, since you all took the time to submit, I'd like to at least give some brief thoughts on each one. So, let's start from the top:
Rhys DeAnno's The Heart of Stall: Stall is something that is brought up during the concept stage of most CAP projects, and normally I am not too big a fan of it. However, I do think that you have made this a bit more interesting than previous such concepts by specifically stating that you want this Pokemon to not just be a good addition to stall teams, but to be the defining element of them: an archetype defining Pokemon in the same vein as weather starters. On the one hand, this take us out of the "let's make a stall Pokemon and see what happens" mindset and makes us think a lot more about general team archetypes, which I feel is a much more interesting route to take. However, this is also a very dangerous concept to attempt. By its very nature we would be trying to make something that is on the same level of Pokemon that people have been arguing over whether to ban or not for years. I don't think this itself is reason not to do it, but I would like to see more details on what we would want to be getting out of it before trying such a thing. I think the concepts biggest strength would be the focus on archetypes, so I would suggest that, especially in the questions section, you go more into what there is to learn regarding team types specifically, and not just things that apply to making a good staller.
Deck Knight's Climate Control: While this could potentially be interesting, the problem I have with a concept like this is that I simply can't see it working. I know this was brought up to you on IRC last night, but while the goal of the concept seems to be to help get rid of weather, in reality, a Pokemon designed to do the job you want would simply be used by weather teams to help beat other weather teams. And, of course, there is the problem that this practically necessitates a specific ability. I'm not the biggest fan of trapping in general, but I will admit that it could be interesting to look at. However when framed around the weather wars, I can't really see it doing what is intended at all.
Yilx's The Big Dipper: I really like this one. Wallbreaking is something everyone thinks they know something about, but the focus on breaking team cores, rather than individual walls, especially when going about it in ways other than pure power, is not really something that I feel we have ever looked all that far into. The biggest strength of this concept in my mind though is the questions. In them, it is clearly laid out exactly the kinds of things we will be looking into with this concept. Investigating what cores really are, or what makes something a wallbreaker are wonderful things for us to think about.
skr1214's Number Cruncher: Honestly, I'm not really sure what you are trying to get at with this concept. Numbers and math are very important to the game of competitive Pokemon, true enough, but we look into such number to some extent every single project. I feel there could be something interesting buried in there, but you will definitely have to be more specific, as right now, I really have no idea what the goals of the concept are, much less how one would even think to start going about accomplishing them.
GatoDelFuego's Chill Pill: Like with the Heart of Stall concept above, this is an attempt to improve stall, but not necessarily through simply making a good stall Pokemon. However, if you want this concept to shine, I think you need to emphasize how you want to go about this more. Specifically, I would like to see more detail regarding those first two questions you ask. Looking in detail at negative momentum and free turns is a lot more in depth of a topic than simply looking at how to make a good stall Pokemon. My main concern here is that this would venture over into territory that we already looked at back in gen V CAP 1, Tomohawk, whose concept was about momentum.
Rayquaza_'s Compact Movepool: This is kind of an overly simple concept. Make a Pokemon with a smallish movepool that is not bad. I simply don't see us getting that much out of this. I think the best way to explain what I mean in a way that is also applicable to other concepts would be to point at the questions. Three of the four are more about if it is possible or what we will need to do to make it possible than anything that which the answer to would be something we are interested in learning. That being said, I will point to the last question as something that is definitely better than the others. While I that is not enough to alone justify this concept, an investigation surrounding the "4 moveslot syndrome" would have a lot more merit to it, as it would be looking for information that would be applicable across all of competitive Pokemon.
Base Speed's Type Equalizer: Like with Yilx's concept above, I think your first couple of questions really seem to get it. Looking at what actually makes types good or not, and the trends that surround them, both in general and in the OU metagame could definitely be interesting. That being said, while it is different in concept, I feel that the goals are very similar to those of the concept for gen V CAP 3, Mollux. While Mollux focused more on bad types than good ones, the ideas about type quality are the same. I'd suggest that you try and differentiate a bit more by going it to detail on how we would attempt to go about it. I think that the concept is a bit vague, and would benefit from having a bit more direction so we can more clearly know what to expect and how by doing this we will be learning things not covered in previous projects.
forestflamerunner's Ability Matchmaker: So, this is pretty much the same concept that was chosen back for gen IV CAP 8, Cyclohm. Now that itself is not an inherent problem, but I don't particularly find this concept all that interesting. While there are plenty of ways such a project could go, in the end, none of them really have a goal in mind. All of them are about taking an ability, throwing them on a Pokemon, making it OU, and seeing what happens, which, as I stated in my first post, is not really the kind of road I want to go down with this project.
The Unlucky one's Ultimate Priority Abuser: I think this concept has some of the same problems as some of the above such as Compact Movepool and Ability Matchmaker. It seems like this is too much about making a Pokemon that does stuff with priority without any really goal in mind for what we want to get out of that. Once more, I will point to the questions section as the key evidence of a problem. As I said up about Compact Movepool, most questions here are simply of the "what will happen when we do this" variety. Questions like these don't give us any sort of goal to strive for.
jc104's Weather Balancer: Well, first off, to address the top of your post, I want to say that what I am asking for is less about concept type and more about concept presentation. I want to see that people have ideas about what specifically we should be trying to learn about with it, as vague concepts have cause us problems in the past. That being said, I think your concept does a good job of this. Of all the weather concepts I have seen throughout the past few CAP projects, this is probably my favorite. The biggest flaw in a lot of weather concepts is that they assume that one Pokemon can do way more than it should be reasonably be able to do. Stopping weather in a single Pokemon is simply impossible. That's what I like about this, it admits that and instead tries to slightly impact some of the weathers in a way that will make all of them more balanced. Additionally, this specifically looks at team types rather than a lot of weather related things which spend too much time focusing on the starters alone. While I have always felt that weather concepts are always somewhat limited, I think this is a very well made concept that, if it is a road we want to take, is quite possibly the best way to go about it.
LightningLord2's Mind Master: Prediction has always been something that interests me, however, as you said yourself, this concept seems very similar to the one we just did for Aurumoth. If you are looking to improve it, I would definitely try and find a way to differentiate it more.
noobiess's Behind Bars: Honestly, this one I just don't see working. While interesting, Imprison is just a mediocre move. You need a decent movepool to make use of it well, but if you have a decent movepool you likely have better things to do. It's simply too limited of a move for us to get much out of.
GRs Cousin's Frostbite: Freeze huh. Interesting. However, this is another one of those concepts that sounds cool in theory but I can't ever see it turning out well. Without resorting to custom mechanics (some of which are now against the rules and all of which I just generally hate), the best we can ever hope to achieve is around a 20% freeze rate. People complain all the time about 70% not being reliable, so 20 is just not gonna cut it.
scorpdestroyer's All Hail Hail: Well, to be frank, I love hail as a weather and think that finding a way for hail to be relevant in the OU metagame would be awesome. However, I have a hard time believing that we would get more out of this than something like the Weather Balancer concept above. I have always thought hail could make a good concept, but I think you would need to focus more on what making hail better could serve to teach us about weather itself or the metagame as a whole.
Aerophoenix's Psych Out: Mind games are an awesome part of competitive games that are rarely analyzed to their full extent. Concepts like this have popped up the past few projects, and I have always been a supporter of them due to the potential they have for teaching us things that you simply cannot get out of math or statistical analysis. As I have been doing a lot, I want to once more point to the questions as a good measure of the concept. I feel you hit a lot of the right notes with these. They are complex questions that are not simply a matter of "let's try it and see". However, I am a bit concerned in that even with these good questions there is a bit of vagueness in what the end goal is. I'd like to see a bit more about what things we should be looking to get out of the process discussions themselves, and not just overall conclusions we can draw based on the success, or lack thereof, of the final result. What you have now is definitely a good base though.
The Steam Punk's The Perfect Gimmick: Probably the biggest problem here is that it focuses on gimmicks, which by their very nature have problems competing. If they were good, they wouldn't be considered a gimmick. The only real exception here is probably Wobbuffet. However, even with something like that, I simply do not see us getting much out of the process.
Lamoprigma's Complete Focus: This concept is way too vague right now. Its true that highly specialized Pokemon rarely take the spotlight in the competitive metagame. The majority of threats are bulky attackers who are very much the opposite of this idea. However, this concept suffers from a lack of focus and has no real goal for us to aim for.
Unitas's One-Timer: This is another concept that seems to suffer from a lack of focus. Being able to do something quickly is a cool idea, but why would something that is good when it comes in suddenly stop being good later? It seems to me like this concept is thinking too much about trying to change the metagame, and not enough about the why or the how.
ganj4lF's Offense-breaker: So I think this one is a pretty cool idea. Bulky offense is the norm in most of our metagames, with more supportive and hyper-O type threats filling out the rest. Very few Pokemon can brag about the ability to take anything, and among those Pokemon who are used for the ability to take hits, most of them are only used because they also can provide support. Learning more about the role of pure, non-supportive, defense could be very interesting and may help explain why some existing Pokemon see the usage, or lack thereof, that they do.
And... that's the end of page one. I need to take a short break from typing, but I will get to responding to the rest in a bit.
EDIT: oh, and to anyone who's concept I talked about above made aditional comments in a later post, I will be sure to look them over too.