I mounted the seat this morning. Nothing very high tech, but still a minor milestone.
I was about to bend some stock steel bar into brackets to hold the seat, when a light bulb went on. I would basically be recreating single-hole conduit clamps, so why not just buy some of those? These would make the task of clamping the seat to the frame pretty easy.
I hit the conduit clamps with some dark gray paint to make them less noticeable, then I glued strips of 3mm neoprene inside them to give them a snug fit and protect the frame once it gets painted.
I initially tried attaching the clamps to the plastic seat base with self-tapping screws, but that was clearly the wrong way to go. So, I disassembled the seat shell from the base and installed rivnuts into the seat base from above. Even though they’re intended for metal plate, they expanded out into the HDPE base material nicely. I could then use 6mm bolts to snug everything up from underneath.
The weight of the seat sits on four plastic furniture feet to protect both the frame and the seat cover snaps.