I would personally remove the transom adapter plate so that you can access the hole easily. I would then drill the hole slightly larger than it's current diameter and then get a wooden dowel that fits tightly in the newly drilled hole. Then, put a liberal amount of wood glue on the dowel and tap it in the hole, it should be a tight enough fit to require being tapped in. (you might want to pre-cut the dowel to length so there is no overhang on the inside or outside of the boat)
Then once the wood glue has dried, cut yourself a nice 1"x1" piece of fiberglass mat and resin it on the inside of the boat to make sure your seal is perfect. Then place the transom adapter plate back on and mark your new hole. Pre-drill the hole and then insert a new screw, but make sure the new one is stainless.
As mentioned above, thru-bolting would probably work also, but getting a wrench on the inside nut will probably be close to impossible.
