Alright, update.
After tracing the whole fuelling harness back to the wiring diagram and having 12V and grounds everywhere they needed to be on the LH2.2 ECU and fuel relay. I connected the knock sensor, no luck, but then swapped the ignition computer and had her fire up.
From the wiring diagram, not quite sure how the ICU could have caused problems with fueling while having the spark working but I'm not going to complain about it working now.
Time to throw her all back together and hope that plugging in the intake + exhaust sensors will sort out her wanting to idle at 2000 rpm.