From the sketch I showed in the previous log, Fusion says that the belt length I need is 237.98mm... essentially 238mm. So I just searched "238mm belt" and coincidentally enough, such belts exist:

I've seen these belts before. I just didn't know that they specifically came in 238mm loops.

The black ones come with a thick looking groove on the underside, which is probably good for the sliding straights but not exactly ideal for the gear-teeth pulley.

The orange ones are slightly cheaper, and because they transmit more light, it's much harder to guage if the underside profile is the same as the black, but it's probably safe to assume so. What I do know is that the black one is rubber and the orange is polyuetherane.

Unfortunately, both of these are 3.2-3.3mm thick, which is almost double the thickness that I'm looking for.

It looks flexible enough:

Looking at what this belt attaches to, the minimum turn radius might be OK if the smaller pulley is 19.5mm:

It also seems self-centering, meaning that I wouldn't need the flange and so I could probably tweak the gears to use something like this:

12T+24T keeps ratios in nice integer values, though I can't find a tight-fit variant:

The final height is 24.5mm, which isn't ideal but doesn't fail any downstream solutions.