I'm waiting to see if anyone suggests to look for the reason for the
loose bolts, like rotten plywood core. So far there is a lot of good
info on backing plates.

Out drive boats are usually built with a plywood core in the transom,
because of the loads the transom takes. I doubt you'll find foam.

If you have some rot, there's no choice on the fix. Backing plates
isn't it.
Jim