[ChuckDriver]

Dan, my seat looked the same when I removed the covers and foam.

The black square on the bottom on mine was rubber and still in perfect shape, I just cleaned it up and reinstalled it. You could easy reproduce it with an old tire tube or other rubber material.

All of the springs were removed from my back and bottom. That made it easy to cut the back down before using the wood and foam to replace the springs.

It looks like the nut plates are missing in the large holes on your seat bottom. They must be there for you to attach the back to it.

You are right, the bolts have a large head and shank on them that allows the back to pivot on. If you need a pic let me know and I'll pull one of mine out for you.