After some months working on this, and seeing the LEDs blink again (it took an embarrassingly long time to realise they were pulled high) I was satisfied I could take a short break from it. I will complete the repair by fully testing it and running the UART Monitor program.
Adeeper A deeper look at the Alesis chip: It is possible that it is a pre-programmed CPLD, but that it has JTAG access. More likely it's an ASIC rather than OTP CPLD or GAL, PAL. Still though, it would be interesting to reveal something about it. As I said it's not on the JTAG chain here anyway.
I will update this when the device is fully tested. For now, be assured that it's back together, repaired, and starting to boot. There could be some small issues, which can be discovered and fixed with the UART function. I could only continue the marathon with a reboot myself.