I did the same thing. I was confident my fiberglass work of 3 layers on the outside and inside was strong enough. A fiberglass expert looked at my project and recommended that I fabricate some knees connecting the stringers to the transom. You can see a picture here.
http://www.theboatzone.com/gallery/briguy/briguy21
I used corecell and a biaxel/matt cloth. Its really strong now.