a 9.9 hp on a 12x36? - You'll be flying!
Looks like a good boat.
If it was me and I was putting a nice 9.9 hp on it, I'd glue two pieces of 3/4 inch plywood together and cut a full transom for the boat. Install it to the boat well. Brace that against the rear seat with a few braces. And I'd build some braces from the transom to the sides of the boat. That might keep some of the flex (popping) down - especially with 10 horses back there.