That is quite interesting.
Going back to your original video, I think this is an issue with the idle air control valve circuit - or, the DME is not getting a signal telling it the throttle plate is at idle. It is behaving as if the IACV isn't actuating at all. If it was something else you would have problems at all throttle positions, not just at idle. Clearly it revs up just fine. So it's an air problem.
<del>Have you checked the throttle position switch per the workshop manual to ensure the numbers are in spec? You should then confirm with the durametric that the throttle plate angle checks out OK. These cars have a dynamic TPS idle setting so there really isn't anything to set - but if the TPS is wonky - it could be sending erratic data back to the ECU messing with the idle mixture. </del>
Ignore above - forgot that the Durametric allows you to check to idle valve directly. Use your Durametric to make sure IACV (Idle air control valve) is fluctuating appropriately and that throttle plate angle checks out OK. It's still possible that you could have a sluggish IACV when cold and even though it's reporting a certain % to the Durametric it isn't actually opening to that setting. Especially as your car sat for a while. A cleaning may still be in order. It probably isn't a problem with the actual primary or secondary windings on the idle valve because that would show up as a fault code.
I would also use your Durametric to see what voltage is both right before you shut it off and immediately after (told you that thing would be useful). Wondering if there is a voltage fluctuation at idle that somehow "clears up" when you reset the signal to the DME by turning the ignition off and back on - taking into account that you did of course just swap out the voltage regulator.
I'm not sure but you might be able to use the "Actuation" tab on the Durametric to force the IACV open. Can't recall if that's an option for our cars. That would be interesting to see how the engine responds.
It totally makes sense to try running it with the OEM - nonsolid state - DME relay to see if there is something weird with how that the SS unit is sending its signal to the ECU.
Do you know if you have the stock ECU chip or aftermarket?
Does it completely go away when the car is at operating temp?
As always, JMO. Im just an amateur with a copy of the workshop manual who likes thinking about other peoples 968 woes