I wish I you had posted this 2 weeks earlier......I have been working on the same fix but your documentation is awesome!
My wife recommended I cut the Styrofoam seat with an electric carving knife, it cut like butter and easily maintained the chalk line. I took out a 4 inch section (from the center) in order to preserve the curvature of the top of the back rest. We reconnected the 2 pieces with carpet glue and wood dowels. (Suggested by my wife also)
We added a 1/2 marine grade plywood base to the bottom of the Styrofoam to create a stronger base.
we used Lowes paint sticks to replace the wood staple strips on the Styrofoam, perfect match on the size and they were held in with liquid nails.
We used plastic cups to measure the height so we could build pvc pedestals (6) to use as feet.
Our intention was to get the seat off the floor and create some (not much) under seat storage.
I'm going to try and post some pictures of the process and a final when I can get one.