re: coring the transom
Just use a regular old drill bit. Drill in the center, toward the bottom. Near the drain plug. And take a couple moving up. Put a piece of tape around the drill bit to indicate about a 1" depth, or use a bit that only sticks about 1" out of the drill. I would use about a quarter inch bit. Look for dry blonde colored shavings. Reddish colored damp shavings are on their way to rotting. Rotted shavings are obvious.