Bridle/Traveler Screweye Screw Trouble

I am having trouble with a traveler replacement on what I am 99% sure is a 1972 Sunfish. The screws on the screw eyes just keep turning without coming out. I have looked at the Youtube videos and repair descriptions on this forum, and I understand that the fastener should be a screw into a backing block. Assuming that there is a single backing block per screw eye then the block should not turn inside the hull because the second screw should hold it. Maybe there are separate backing blocks...

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