You may want to start a thread or piggyback on this one so others can chime in and maybe learn too.
https://rennlist.com/forums/996-foru...olenoid-5.html
Starting in post #70, I mentioned a light bulb method to troubleshoot intermittent problems. That way you cut the problem in halves - the control side and the power side. It's some work to wire the bulb but it could give us more clues.
The control side is everything from the key immo pill, immo, dme, to the relay. The power side is the ignition switch, relay and the starter.
You case is strange that when the starter engagaes, it only spins one revolution or so and then quits (if I understand you correctly). And now it's even harder to explain after you said it's not temperature related.
Did it ever work better since the ecu/immo repair? Can you send those back to them to check again? A video showing the instrument cluster during a failed start up will help.