Step 1: The Controller...
The requrements are four push-buttons and an analogue stick. I found a pair of these USB Playstation-style controllers and as they were cheap, bought them on spec.
I'm not the first to do this mod. It's convered a couple of times elsewhere on the 'net, either by buying a black box (just plug and play), or by hacking up a little analog circuit to do the job. Here, I'll do the conversion with as few extra components as possible.
Turns out, the pack I purchased contained a pair of 'real' fake PSX controllers with the cables siamesed together into a single USB adapter box, inside which turns out to be a 'glop-top', presumably an ASIC dedicated for the task.