You did a nice job designing the seat frame! Yes, you can make the reverse of the pads or cushions or whatever you want to call them by using a thin piece of plywood, ( or my choice would be 1/4" PVC foamboard, but I keep that at my shop all the time.) and staple to it. Glueing the fabric would be not be necessary.
The seat bottom area could be held in place by drilling holes through the frame and "T" nuts installed in the plywood under the cushion foam. Then you could bolt the seat bottom down from the under side of the frame.
I would pad the outside and inside of the side bolster areas and the back side of the frame with 1/4" closed cell foam (brand name Volara). This is pretty rigid, so it is good strong padding with less thickness and less weight. You will need to glue this stuff to the frame. Be sure to scuff the shiny outside of the Volara so glue adheres to it better.
No one lives forever, the trick is creating something that will.