If it were me,
2x2s are fine, if you can keep them straight. There's no load being supported, so you don't need 2x4's or more.
I'd frame it when yr framing everything else. No reason to do dwall twice. Too messy.
Not sure I understand how yr beam runs. If it can be hidden by making a 12" soffit that runs flush to the cab faces, my vote is for that. I'd put a veneer and some molding on it to match the cabinet face. It'll actually make yr cabs look taller and built-in.