I had a 228D Flagstaff, the same as yours. Flagstaff and Rockwood are like GMC and Chevy.
I had the same. The hinged wooden board flips up and leans in to the canvas. The cushion is of course taller than the board and does as well.
What compounds the issue is when you lean back the wood backboard hits the top of the slideout and if you push back at all the hinge acts as a fulcrum and pushes the seat away from the back. This will pop the light wood panel off the front of the seat.
I doubled up the light wood of the seat frame along the sides and front of the seat then used some flat steel about to make a squared off "S" shape hooked both the expanded frame I made and over the leading edge of the seat bottom. This prevented it from sliding forward. Put them about 2 inches from each end.
This is a profile/side view. The top "open" part of the hook captures the seat bottom plywood and keeps it in place from sliding. I screwed them in to the seat frame to hold in place. It will take some practice because with this in place it will have to be lifted up from the rear to pull up/out and slid out of the hook.