Lay the case/mobo down on a solid flat surface,
support underneath the mobo tray by removing the side panel and positioning the mobo tray over a suitable height book, so it all 'sits' on the book
put the other screws back in reasonably tight to ease the pressure on the one sticky screw
push the screw driver down very firmly on the bad screw to increase the grip/torque,
the book underneath will take the extra force without bending your mobo/case
if this doesn't help then drilling is the way to go.
This is absolutely what I should have said, but assumed it would not be possible with whatever case you have. Good advice.