Woodworking tips to fix a stripped MDF screw hole WITHOUT glue

Please note: I see some other very similar questions but the recommended answers all suggest using glue in some form. I can’t use glue as part of this solution!

I have a workbench that, on the end cap, has an upside down screw that keeps a piece of wood (on my bench) fastened to an MDF board. The problem is that I’ve had to move the workbench many times over the years, and each time I do, I need to unscrew and rescrew this upside down screw, and the residual wear-and-tear has started to strip both the wooden and MDF screw holes.

So now, I can pretty much just push the screw into place, and its not really doing its job, and the two pieces of wood come apart easily.

What can I do to make the screw "stick" and properly secure the two pieces of wood together?

I absolutely have to keep the existing MDF board in place; I cannot replace it. I do not want to use any type of glue as that would be permanent. And I am open to using a thicker "gauge" screw but I’m worried this might cause the board and MDF to crack or break apart and, besides, I’m not sure if there are any other woodworking tricks this community could teach me here that would solve the problem without needing new hardware! Thanks in advance!