You're right, those springs are pretty well worthless. Screw or bolt ( bolts would be best, and be sure to countersink the bolt heads) the plywood frame on the back of the old seat frame towards the rear of the car. This has the added benefit of making the seat frame stronger. Staple the elastic webbing on the front side of the plywood towards the front of the car. Then you need to pad the back of the plywood frame before you pull the cover over the new foam. Be sure you sand down the outside edges of the plywood frame just enough so the edges are not sharp. If you want, you can staple the fabric onto the plywood frame instead of sewing the seat back all together and pulling it over the frame. Then cover the seat back with an upholstered panel, just like a door panel. The early 60's Mustang seat backs were done like this with a panel to finish them off. If this doesn't make sense to you, just ask more questions.
No one lives forever, the trick is creating something that will.