Update:
I got a chance to grab half an hour in the garage tonight, so I thought I would try swapping the starter again. When I took it off, the ring gear just fell off the flywheel.
I can only assume that the company that lightened it have machined away whatever holds the ring gear in place. Brian, you mentioned dowels?
I have a spare flywheel on my spare engine, so now I have to pull the engine out again and swap the flywheel

. I don't have any way to get the car high enough off the ground to remove the gearbox on its own.
I dread to think what would have happened if it had come off at speed on the motorway.