Jim, that's real similar to what I have. I ended up adding a 1/8" plywood backing peice to that vertical backrest support, and adding cleats to the hull and under the deck to attach it to. Then I hung the back rest on webbing, so it can be lifted up out of the way and storage behind is accessable. If you didnt leave any storage behind there, then gluing the backrest to the vertical support would be a cleaner installation.

I had to add the wood backing because the back rest wouldnt stay in place without it. If I were doing it again, I'd try to support it from each end of the bac rest, toward the sides of the coaming, so that as it's lifted up you can access the whole width of the boat right behind the seat.