While Stall is better in comparison to SVAAA given the potency of HO within the tier and also gaining extra tools like double Regen and MBounce I wouldn't call it a tier-dominating force from anecdotal experience on ladder as it experiences the same issues innate to the archetype as it does everywhere, that being its passivity and lack of leeway against mons that pressure it. I can't outline any specific breakers since you haven't outlined any mons except Chansey and some abilities but you can look at the VR and there are many strong breakers that can pressure Stall such as Psyshock Tapu Lele, Walking Wake (which can pressure greatly with strong WBalls and Knock Off, particularly potent on SpikeStack BO/Balance styles), ISword MMawile/MMedi, Gapdos, Deoxys-S, Pursuit users such as Bisharp and MTar, the variety of Trick mons such as Fini, Mew, etc* that can cripple annoying threats, hazard setters that threaten MSab (eg Heatran), the whole mechanic of ZMoves and so on.
This is unfortunately not likely to happen as to become a permanent ladder would probably require Admin approval and they are generally quite strict about adding new Permaladders without a very strong case (even high plays isn't entirely convincing as other high-play temporary ladders like in the SVOMs sections have proven to see a significant decay in plays after they become a permaladder eg SP) so unfortunately you'll have to wait at least another 6 months for AAA to be back in the pool again, but hey if plays continue to be sustained for the third month maybe it wouldn't be as impossible perhaps...