Atlantic Suitcase Screw Removal

I have some older Atlantic two wheel rolling suitcases in need of
wheel replacement. There are what appears to be phillips head screws
on the outside of the suitcase that go into in attachment inside,
behind the lining.

I can get to the attachment, and when trying to remove the screws I
fail. I can hold part of the attachment with plyers and the screw
rotates, but won't back out. I have tried pulling on the attachment
while turning the screw, which should help with stripped threads, but
no removal.

Does anybody have any suggestions.

Thanks,

Tom Williams
tomwms at comcast (dot) net