I'd only want shields from AST/SCH to stack if they were both nerfed to appropriate levels to compensate and if WHM got an overheal cooldown to help with their lack of mitigation. That would mean SCH would give up Critlo and Noct would have its shield potency normalized to match. Succor AND Noct Helios would both be nerfed to 150 shield potency, which is what it was in HW. Hell I'd be fine if it was nerfed further than that.
The only reason I don't want your exact proposed changes is because I feel that AST should get the stance swap as a pair of cooldowns, not as an always on thing. Having to pick between the two is a meaningful choice and should continue to matter.
The two cooldowns I'd propose are as thus, along with two other notes to help facilitate their use:
1) An Emergency Tactics-style stance swap for the next Aspected spell you cast. Just the swap. No additional benefits. Lasts 15s or until used. 20s Cooldown. Functionally very similar to Emergency Tactics.
2) Take Largesse's 20% healing potency and swap the AST into the other Sect temporarily while benefiting from the healing bonus. No additional benefits. Same 20s duration. 120s cooldown.
3) These abilities stack together, allowing you to get 1-2 spells in your original sect under the healing bonus.
4) Remove the healing potencies on both sects and balance all of the aspected and non-aspected healing spells around a single baseline value. This can be between WHM and SCH in healing potency on the non-aspected spells, and equal on the aspected ones.