How do I handle ground wires in 2-gang box with circuits coming from separate breaker boxes
Good question, but pause to think: What if all your wiring was in EMT metal conduit? (In which the conduit is the ground).  There'd be no choice to bond the grounds, and thus, it is OK. 

This question is even easier since you are working out of a sub-panel, which already has its ground bonded to the main panel; that is, one ground rod for the whole house.  I have a facility where the 120/240v is served out of two main panels, each with its own supply transformer and its own ground.  Circuits from both main panels go into a spiderweb of EMT, and while the neutrals never cross, the EMT certainly does, which means the ground does.  What's more, the EMT is attached to an all steel building via girder clamps that are entirely made of metal. It would be impractical to separate the grounds.  All this to say: If I am allowed to mix grounds, you certainly are.