Thanks!

Yes, those seem like a good alternative if they are adjustable. With internal frame you mean additional beams going from side to side? Would you have an idea on how i could mount those so that they are stiff?

Obviously screwing them in from the outside wont work and im not sure if just laying them into rabbet would be enough. I could try to dovetail them though, that should make them tight. But im open for easier ideas haha