I decided to mess with these eyelets that are on the back of the sunfish. The one screw head broke off.
I got two others out fine. These are not wood screws but some sort of self tapping machine screw. This is a 1998 era Person built hull.
I am making an assumption it is just going into thick fiberglass.
Does anyone have experience with this problem and which solution works?
thanks
I have experience with this, and I've found...
If it ain't broke, don't try to fix it!
OK...
...Solutions...
1) You can go to the next size machine screw, drill for
that size, and use a tap to rethread the plate.
2) Move the eye strap over ⅜- to ½-inch, and drill/tap for the same-sized machine screw. Drill slowly, starting with smaller sizes—we don't want the plate to dislodge or bend

. Put anti-corrosion paste in the hole and on the machine screw. (Or waterproof grease, if that is what's handy).
3) Access the eye strap's underside by cutting through the hull bottom. Re-tap the existing hole or enlarge the hole for a nut and bolt of the same size. Tighten the bolt and rebuild the hole in the bottom.
4) I see one screw head has broken off.

Since the screw is stainless steel, drilling it out is quite an exercise!

I'd keep the existing (good) machine screw, and rotate the eye strap to a new location, and proceed as below:
Insert a
Toggler™ toggle-anchor ($5). To do so, drill out the hole
and backing plate to fit. Reverse it on its plastic insertion device (included), secure it (for now) with epoxy. Wrap a threaded rod (one that fits the new threads) with electrical tape, insert it, and back-fill the hole with an epoxy mix. Once cured, remove the threaded rod and install the eye strap back into its new location.

No taps needed.
To make the other side match is more work, but an option.
6) Reverse both sides:
I don't see any harm in using sheet metal screws—providing the plate is present and drill-able.