I have no idea what to suggest as far as what class-features should be functional with mechs. Magic could be interesting, though without other options I'd be concerned it would make casters the go-to for pilots. Solarians could maybe manifest through the mech/its weapons? Maybe Mechanics could control larger, mech-launched drones while piloting (if they chose a drone), or the ability to interface directly with their mech (if exocortex)!
As far as 'stunts', I've always been a fan of mobility. Orbital drops, jump-jets, that sort of thing. For instance, I'm reminded of the WH40K Rogue Trader RPG, specifically the Tau sourcebook. One of the "Classified Competencies" that a Tau character could choose allowed them to, as a reaction to an attack on an ally, take a move action to dash in front of them and take the hit themselves.
(Also, I'd definitely like to see a starship module allowing orbital drops. Maybe separate from any "mech-suit storage" module, or a sidegrade from it, so you have to want it?)
Regardless, godspeed! I've been practically *vibrating* with excitement since you mentioned this project in another thread.