Self-tapping screws are TOUGH on any substrate, wood or synthetic, as the teeth that hold, are still cutting anytime the material moves. If you could, it would be best to secure with a through bolt, provided it would work for you and looked OK. You could do every 3rd one or oevery other one, just so the bolts take the force. By the way, this is how wood boats or wooden boats get rot inside, as the teeth finally wear the hole oversize so rainwater gets in ... dries out ... gets in .. .dries out ... and that wet/dry cycle causes rot.
If you had adhesive-lined heatshrink on hand, put a small piece on the screw, or use next size larger screw (say #10 versus #8), but file the teeth to less of an sharp edge and you might need to file the head to fit the recess of finish washer, unless the larger corresponding finish washer works (if used that is). Or, fill the hole with toothpicks (an old time trick!) and maybe a dab of LifeCaulk or 3M 5200,even though this stuff doesn't stick to poly materials well, if at all. I have used the heatshrink and larger FILED screw approach and it removed the problem forever. But, my use of screws is limited, haha!