You know, that's an interesting point; 'should be better in the core than when it's not in it'. But I feel like Regenerator fits that bill down to a T. With Latias' support, it goes from breaking even with Stealth Rocks, to being able to take a Shadow Ball, hit back, and switch out, healing off most of the damage. I'd say that's 'better in the core'.
On No Guard, I'm concerned that we're going from a Sacred Fire comparable Serene Grace burn chance, to a move that's just as powerful as Sacred Fire, but burns all the time. I'd say that's just as, if not, more OP than a strong Contrary Overheat. I mean, look at Machamp and Golurk; while they both have Dynamicpunch, that's used primarially for shuffling the opposing team; confusion isn't persistent, which just makes it a sweet BP move with a fun secondary effect. Something that literally WILL ALWAYS BURN, seems cheap, and entirely destroys the utility of moves such as Will-o-Wisp, entirely kicks Entei's niche in the ass, AND has no synergy with Latias and Lucario that wouldn't be better spent somewhere else. Serene Grace has upsides and downsides, the upside being a de-facto Sacred Fire off two STABs, the downside being their lacklustre individual BPs.
Rattled is an interesting choice. It has great synergy with Latias, and I'd say probably plays to the concept of working better within the core than without it; as Latias is one of the only Psychics in the metagame, and the one people rely on super-effectively hitting to take down, you'd be able to grab those Rattled boosts at several times throughout the game. My issue is, it doesn't help directly with Aegislash, but more capitalizes off him, but at the same time, if CAP can threaten it into switching out immediately, you now have a fast will-o-wisp/scald/lava plume to weaken physical attackers before they can do anything. My issue with it is situationality. Sure, you get the ability to switch into Knock Offs and come out the better for it, but prediction is absolutely key, and the utility gained from it could be accomplished with Prankster, without the guesswork.
I just remembered something I was thinking of in the threat discussion page. As previously mentioned, Knock Off is absolutely ubiquitous in the metagame, and Latias hates that possibly even more than Pursuit. Lucario doesn't exactly enjoy it either; sure he gets an attack boost if Justified, but he loses his life orb, and loses that boost if he's forced to switch out. I propose Unburden as an ability for this CAP, for several reasons:
1. To counter the ubiquity of Knock Off and support Latias.
2. To provide versatility of item-based strategy, allowing the direct countering of specific threats.
3. To give CAP a one-time boost that lets it seriously put a dent in the opposition, which Lucario can clean up with Extremespeed.
Now, point 1 is self-explanatory, but for point 2, I'm going to rattle off a couple examples; please don't misconstrue this as poll jumping, I'm more just brainstorming the utility that can be provided by this set if we actually focused on building a moveset that's advantageous to this playstyle. All moves are absolutely subject to the later stages in the CAP. And some of these sets plain suck, but they do illustrate the enormous versatility of this.
- Simple Sitrus Berry set; can take a Shadow Ball more, proceed to 2HKO Aegislash, and be able to comfortably outspeed any possible switchin, bar priority.
- White Herb Overheat set; can threaten Aegislash with a 140BP STAB Super Effective move, and gets a speed boost AND no Sp.Att reduction, if he switches out or not, preserves offensive momentum.
- Maranga Berry set, once again focusing on taking more Shadow Balls. (i wish this berry was good)
- ChestoRest boosting set (Calm Mind or Bulk Up could work fine; Coil?)
- Fling - status spread, or high powered Dark type utility move. (Hit opposing latias?)
- SubBerry sets, to double speed and 1.5 times whichever attacking stat.
- Red Card set; can take a hit from Aegislash and switch it out for something else that you now outspeed.
- Super-effective reducing berries can allow for one-time counters of Excadrill and Lando-T, managing to OHKO in return with a fire/water move.
- Normal Gem Fake Out set.
While it doesn't directly help with countering Aegislash, there are a multitude of strategies that can be used with this ability, giving this CAP the advantage of unpredictability that Contrary or Bulletproof couldn't hope to achieve. In a metagame which is based around testing this pokemon and its teammates, the different sets CAP runs are going to be the absolute make or break for a team, and this ability facilitates this, giving CAP the tools it needs to get past whatever it wants, really.
EDIT: Just another thing I thought about: an Air Balloon set with Unburden would make CAP a pretty hard counter to Lando-T and Excadrill. Food for thought.