Would baking these work? Always prefer to bake if I can

I have baked a similar bean burger. I heat my oven to 400 F (convection bake), then place the patties on a greased baking sheet and cooking them for 25-30 minutes; I turn the patties halfway through the bake.

Yes, they would.
Plenty of baked falafel recipes out there.
Try one on it's own (like a first pancake), in case you need to adjust the batter slightly.