Like Half mentioned - don't use 5200 anywhere you are mating the plate to the hull. You're basically super glueing it if you use that stuff. Wrong application for 5200.
You won't be making a "patch" in option #2. You'll be repairing the hole. The screws, most likely, are 1" long and would not penetrate through the transom. Once you get the "plug" out, use a much larger drill bit (or a dremel sanding drum bit) and chamfer this new hole. The purpose here is to give more surface area for the epoxy (poly is fine, if you prefer) and glass to bond. Pre-cut a couple small pieces of glass for this chamfered area. Once piece will be the size of the chamfered area and then a couple more pieces are cut to successively smaller sizes to build up the area flat. For the hole, pre-wet it (a couple times over the course of about 15 minutes so the resin soaks into the core) with a pipe cleaner. Also pre-wet some scraps of glass to be pushed into the hole, as well. The trick is to avoid air pockets in the hole - which you can do by using a syringe and filling from the backside of the hole. Have a good piece of tape ready to go and cover the hole to keep the resin from leaking out. Let that gel up and then you can remove the tape and finish with the pre-cut pieces of glass. Once it's cured, lightly sand the area so it's flush with the surrounding area. When you're done, this will actually be an improvement over the original way that GW installed it.
That's "ideal" (in my book). But... you could also pre-wet the hole and then fill with thickened resin - that will be quite good, as well. But you still want to use a syringe to avoid air pockets.
Those are just two thoughts off the top of my head - other ways can work, as well.
Pre-wetting is important to get a good bond inside the hole.
Caulked holes are not a problem functionally... just aesthetically. Unless of course your boat is bottom painted then you won't see it, anyways.