So it now works, but I'm not sure how.
The potentiometer is marked on the board as being for 5V adjustment - but when turned, the 5V rail would jump to 16V intermittently. It's also an odd arrangement - apart from the center pin, the other two connections are made by braid. On top of this, it looks like someone may have been in here before and replaced the 7805.
Figuring that I had nothing to lose, I hit the 7805 connections and the braid with my iron, then remeasured - at which point I could steadily adjust the rail to 5.2V (but no lower). Reconnecting the rest of the boards, it now boots successfully, albeit:
- 18V input to the regulator doesn't seem like a great idea
- 5.2V appears too high
- I don't entirely trust the trimmer
Perhaps the obvious thing to do here therefore is replace the trimmer so that at least the digital parts aren't over-voltaged, but I'm a bit concerned about the lifespan of the regulator. That said, there's a thread in this very forum along these lines here:
https://www.eevblog.com/forum/repair/yamaha-dx7-keyboard-overheating-29v-going-into-7815/.Thanks for all your help so far, anyway - any suggestions before I swap the trimmer and move on?