Cosmic Power (Plus Defend Order, and situationally Magnetic Flux): Sharply raises the user's defenses, lowers Attack and Special Attack. Very useful for walls.
Foul Play: Raises the user's defenses while reducing their vulnerability to Foul Play and Confusion self-hitting. For Klefki, Sableye, etc, Foul Play is now fantastic. It of course ignores drops to the user's own Attack stages.
Shift Gear: Agility+Cosmic Power, with the only loss being your Special Attack drops. Klinklang can ignore that if it likes.
Tail Glow: Nasty Plot+Cosmic Power while reducing vulnerability to Foul Play and Confusion self-hitting. Fantastic.
Anything that sharply raises a defensive stat: Cotton Power, lowers your offenses. Yikes.
Cotton Guard: Raises Defense 4 stages, raises Special Defense, lowers offenses. Holy crap.
Quiver Dance: Sharply raises Special Defense, raises Defense and Speed, reduces vulnerability to Foul Play and Confusion self-hitting. Wow. Keep in mind Volcarona gets Fiery Dance and it has a 50% chance of raising the user's Special Attack, so Volcarona can easily chain a series of attacks without needing to Roost to get its Special Attack back. Oh, and it gets Roost hurrrr.
Focus Energy: If it counts as a set-up move (Pretty sure it does), just give the user a Scope Lens (Or have Super Luck or be using moves with an increased critical hit ratio) and now they lower their offenses (But completely ignore the drop because lol crits) while using Cosmic Power. Nice.
Growth: Cosmic Power. In Sun, Cosmic non-Sun Growth. (+1 to everything except Speed, crit chance, Evasion, and Accuracy) Heck yeah.
Work Up: Cosmic Power.
Swords Dance: Howl+Cosmic Power. Nice.
Nasty Plot: Calm Mind+Harden.
Calm Mind: Amnesia+Harden, lowers vulnerability to Foul Play and Confusion self-hitting.
Bulk Up: Iron Defense+ uuuuh plus, uh, +1 to Special Defense, OK? Lowers Special Attack one stage.
Agility: Cosmic Agility! Lowers offenses though.
Reflect and Light Screen: Wait, are these Status moves or set-up moves?
Accupressure: Cosmic Power+random stat. Lowers offenses, but hey, Shuckle doesn't care.
Amnesia: Drastically raises Special Defense, raises Defense, lowers offenses. Heck yeah.
Hone Claws: Cosmic Power+Accuracy. Attack stays the same. Lose Special Attack. Pretty cool.
Coil: Sharply raise Defense, raise Special Defense, raise Accuracy, Attack stays the same. Lose Special Attack. Better than Hone Claws, of course.
Dragon Dance: Speed+Cosmic Power. Attack stays the same. Pretty cool.
Poison Fang: Now that Toxic lowers your defenses while Poison Fang raises them, might be worth using over Toxic.
Leeching moves: Much more appealing for walls now, since they all double as Cosmic Power. Especially if you can get a maxed critical hit ratio.
Note that Drifblim, Blaziken, Scizor, Swellow, Furret, Beedrill, and of course Smeargle all get both Baton Pass (What happens with it anyway, stats-wise?) and Focus Energy. They'll be huge complements to any Pokemon that wants to wall and has access to leeching moves. Pass off Focus Energy, and leech away with each leech being a Cosmic Power+heal while completely ignoring the offense drops! (Completely if you're holding a Scope Lens, anyway)
Contrary: So now whenever Malamar attacks with any move its defenses lower and its offenses rise. Pass off some Speed boosts to it and murder everything.
Shuckle meanwhile can run Contrary and spam its usual repertoire of Status moves with them all being Cosmic Power too.
Regigigas: Give it Leftovers, start slapping everything with Power Up Punch, stall the heck out of the enemy until your Slow Start ends, start murdering things while basically invincible.
Roar and Whirlwind: Raise your offensive stats while ensuring your opponent doesn't get to use the fact that your defensive stats dropped. (Specifically useful for fast Pokemon)
Circle Throw and Dragon Tail: Keep Cosmic Powering while slamming the enemy through hazards over and over and oh my god over.
Power Up Punch: I already covered this, but its damaging Cosmic Power that retains your Attack. Sweet.
Charge Beam: What I just said about Power Up Punch, but less reliable. And for Special Attack.
Recharge moves: Maybe slightly less terrible, since they raise your defenses in the process?
Acid Spray: Harshly lowers the target's Special Defense while you use Cosmic Power. Their defenses will drop faster than your offense!
Stored Power: Oh my god. Keep in mind that Stored Power only cares about how many stats are above base -it doesn't count stats below base as a negative. So every time you attack with it, it gains BP and you use Cosmic Power.
Punishment: What I just said about Stored Power, but for beating up the opponent. Consider consistently using this over Crunch -after one move most Pokemon will have at least two stages, raising its BP to 100!
Frost Breath and Storm Throw: Cosmic Power and completely ignores the drop to your offensive stats! Also completely ignore the enemy's attempts to raise their defenses!
Seismic Toss and Night Shade: I just covered this.
Clear Smog: Get the enemy's out of control stats back to baseline. And use Cosmic Power.
Volt Switch and U-Turn: Attack and switch out without having to suffer from decreased defenses!
Fake Out: Cosmic Power before the enemy can attack, and in fact preventing them from attacking. Sableye might be justified in running this and Foul Play consistently.
Endeavor: Cosmic Power while dragging your opponent's HP to your own level, totally unimpressed with your Attack and Special Attack drops.
Counter, Mirror Coat, and Metal Burst: Wait, do these count as attacking moves?
Priority attacks, generally: Cosmic Power before the enemy can move!
Chip Away and Sacred Sword: Ignore the enemy's (Potentially huge) defensive boosts while Cosmic Powering. But lower your offenses and actually care. Probably invalidated by Frost Breath and Storm Throw and Critdra and...
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I suspect Shuckle is going to be the king of this meta, with Volcarona possibly king of offense Pokemon. Either that or some of the Frost Breath/Storm Throw Pokemon.
More generally, I anticipate Hazards: The Meta.