After drilling out 6 rivets that held the seat to the frame, off it came:
The top of the frame was actually in very good condition; too bad no one sees the top when the seat is mounted on it. Oh well, paint it is!
I painted the seat frame with gloss black TREMCLAD rust paint. This stuff is amazing. It sticks to anything, and leaves an awesome finish. AND it's cheap (~$6/can).
The next step was to disassemble the entire seat cushion. This involved cutting through the stiching along the periphery of the seat that held the vinyl seat cover to the moulded plastic seat.
After the stiches were removed, I had to peel off the vinyl seat cover that had been glued in place. This wasn't too difficult as the glue was quite old, and came off easily.
Removal of the vinyl covering exposes the underpadding which consists of a thin sheet of foam covering what appeared to be very similar to carpet underpadding (the omelette coloured stuff in the pic below). Thankfully, the foam padding and underpadding was in very good condition, so I was able to reuse it, instead of cutting out new foam. Since the seat is spring loaded anyway, this shouldn't affect the comfort significantly at all.