A wild and crazy thought, Jonathan.
Might the seat cushion in this case be a one piece design?
The seat cushion could have a wood board base with a pad of horsehair etc., on the top, sized so when complete, the board ‘locks’ the seat cushion into the steel pan. The back is just a soft pad with no hard backing. The oil cloth, or similar material, would run from the front edge of the seat back across the seat cushion and then run up the back cushion, forming a sort of hinge between the two section at the bottom rear junction of the two sections.
At the top of the seat back, a light weight cotton or canvas layer is added to the mix. This is stitched in to enclose the seat back pad and prevent it from sagging to the bottom of the seat back over time. The oil cloth material then wraps over the top of the seat back pad and down the back of the seat back cushion to the junction of the back pad and seat pad. It is stitched down the sides only, staying open across the bottom.
This forms a pouch down the back portion of the cushion assembly that is pulled down over the seat back frame to the point where the seat cushion portion can drop down and lock into the steel seat pan.
I notice the seat back can adjust and has a noticeable recline ability. The recline mode might be to make entry to and exit from the drivers seat easier for the driver and the one piece design would enhance sliding in and out of the seat quickly.
Then again, I could be totally out to lunch!
David