What has actually happened to the SS screws that were installed is the three metals that combine to make stainless steel
, which I think are iron, chromium, and a third I forget (could be manganese?) anyway, over time the elements making up the molecules migrate back to elements (there are several theories why, all are 'iffy' and boring) and the iron then rusts away, leaving crystallized chromium. It is brittle difficult to get a drill bit started. However, just below that troublesome layer is plain, undamaged stainless, which will drill if you can hold the bit centered in the hole.
Failure to hold the drill perfectly will result in it running off and damaging, maybe ever cracking, the plastic. A bummer. Possible leak, and more problems. Do not go at this without preparing properly. More on that in a moment.
It is common for only a few of the screws to have gone south, while many others are fine. get at least one good screw out and replace it with quality screws and a good caulk, like Boatlife. Avoid straight silicone if you can.
Once you have completed all the ones you can and have only the rotted shanks left, you can prepare for them. Find a way to see if you can get at the screw tips from inside the boat, where a careful bit of work with a small pair of vice grips might simplify get the dead shanks out. If not, or, if only a few can be cured that way, and you still have to get at the others with a drill bit, you need to get clever.
You say the screws are in oversize holes, which is a blessing. Carefully clean out the hole between the dead shank and the plastic with a sharp scribe or dental pick and measure the hole diameter. go to the local auto parts
store and see if the have some steel brake line that will fit into the hole. Once you find some, cut off an inch of it, deburr it, and press it into a drilled hole in a small block of wood so that about 1/16 of an inch of the tubing is poking through the bottom and the wooden block can sit flat on the plastic with the tube sticking down into the hole. Now you have a jig to prevent damaging the plastic.
Select the largest drill you can that will fit through the tub without binding and carefully, at slow drill speed, clean up the top of the broken screw. It will feel and sound 'crunchy' at first, then smooth out. Stop there.
You should have a clean divot, dead center in the dead shank, which will guide your smaller drill right where you want it. Complete this action on all the broken screws before going to the next step.
Now, stainless steel is tough to drill and gets hot fast, but with sharp, new buts and a little lube, and care, it drills just fine. Too big a drill will leave nothing in the hole but the threads, and that's no good. Too small a drill will either snap off, or not allow the easy-out (screw extractor) in far enough to get a grip. You have to examine the screws you were able to safely remove and select a drill size of exactly the right size.
When you begin drilling into the screws, go slow and keep pulling the drill back to clear the chips. It is possible during this that any old sealer holding the shank will heat up, break loose, and the screw may start sinking. Stop immediately. Have the easy out ready, and quickly try to withdraw the screw. If it sticks partway out, that may just be the old sealer cooling
due to the heatsink effect of the easy out, but the extractor should still overpower it and get the screws out.
This all seems elaborate and tedious. but when you are done, without damage to the plastic or the boat, it will be well worth it, and you'll have a great tale to bore others with during sundown cocktails.