The flex you are seeing is surprising. I have an O'Day 27 (1973) with a 12hp outboard. I have never seen any flex or weakness in the transom, and even use it as a step to get up on the boat sometimes when it's on the hard. I don't specifically remember what (if any) size of backing plate is used, the transom is so sturdy that it has been a long time since I looked.
One caveat: my boat was built as an outboard model (never had an inboard) so it may have different construction than the models with inboards.