right ok, i had 2 possible causes, from what you are saying it has ruled out one possibility.

From what i can gather the engine is being starved at idle, as you have to hold the throttle open to make it idle.

presumably you know what the auxiliary air device is? this allows a certain amount of air to bypass the throttle housing when cold, and it sounds like its not opening up when the engine is cold

personally i would remove it and test it, but if you cannot be arsed or dont feel confident u could just remove the pipe from the throttle housing and try cold starting, although im sure it will rev very high as it will allow too much air flow.

to test it, remove it and you will see a plate inside the unit through the hole, then apply 12v across the wiring plug and u should see the plate move and close up. my guess if yours will already be fully closed when u look inside it?

a lot to take in let me know if thats proving difficult