I like what Tom suggested.
OP, what is the mechanism that walks them out? Are the screws too small for the holes (stripped) or are the two pieces trying to move independently of each other?
Is the "top cap" is moving at the corner? If that is the case, I would gently pry it out with a plastic putty knife or something and insert a long piece of double sided 3m tape to serve as a gasket and lock the pieces together. The stuff is no joke. Run an acetone rag in the gap first to clean. Then put the appropriately sized screws back in, preferably through the strip of tape.
I have used fatter screws before, and when the heads are slightly too big, grind them smaller with sandpaper or a grinding wheel. PIA, but it's only 3 of them. Buy extra because you will mess up a few.
