This concept really intrigued me because there is a lot going on and it will definitely be a challenge, but it will really teach us some interesting things if we prove to be successful.
Now, as it's been stated many times so far, I think water, steel, and dragon should be the focus of our project. I say we do not focus on fighting for on simple reason. There is no dominant play style that revolves around the fighting type. I think focusing on types that the metagame is centralized around will make it easier to find a way to lower the usage of said types.
As to our approach, I do not think we should take a route such as nyttyn's, in focusing on a type that would do well against these common typings. This won't really teach us anything about the metagame except that if a powerful Pokemon is introduced, the Pokemon it has good type matchups against will decrease in usage. I also see this direction being more inclined to fall into the trap of making a super Pokemon, like what happened with auromoth.
I feel the approach we should be taking is finding a Pokemon that can bring a lesser used play style greater effectiveness by covering its weaknesses against the types we are focusing on. after thinking about that for a while, I thought of an example in genesect. Genesect did an excellent job of patching up a sun team's weakness to dragons and rain teams specifically things such as lati@s. the only problem with this example is that genesect also centralized the metagame around itself. The other thing about this example though is that although genesect was a steel type, he made steels less effective by countering dragons, steel types other than heatran, and making sun more viable.
So in conclusion, the focus we should be taking is not on a single Pokemon but on an entire play style, which will make the metagame less centralized around the types that are under question.