So! I finally got around to replacing the MCU (had to wait until I did my next Mouser order). Made a total mess of removing the old one - I lifted a few pads off, but very luckily none of them are used in this circuit! But I got the new MCU soldered on and flashed, and...
Drawing ~117mA on the +12V rail (which is a margin-of-error off from the 110mA listed in the manual), and it runs off my uZeus now too. So excited to have finally got it working, 6 months removed from when I thought I had finished the build!
Thanks so much for your help and advice!