Tickover should be controlled by the IACV (Idle Air Control Valve, on the passenger side of the plenum). The ECU should open this until the engine will idle at the correct speed and then compensate for rapid changes by adjusting the ignition timing.
As long as the IACV is working and can pass enough air the ECU should get the idle speed right.
Is the IACV clean?
If it's duff, you'll find the idle very slow when cold because normally the ECU will aim for a higher idle speed after a cold start but the IACV won't be able to pass the increased amount of air required for a cold engine. You'll find the idle speed increases slowly as the engine warms up and maybe doesn't get compensated when you turn the steering wheel, switch on the A/C, etc. I'm sure this would cause a fault code though, and you state that the idle is stable when you add these loads.
How does the idle speed stabilise when you blip the throttle then release? Does it dip under the normal speed and then recover or does it settle gently to the normal speed?
The IACV has no effect on normal running when you're on the throttle, however.
I could think of a few things it could be (throttle pot, air / water temperature sensors, MAF) but I'm struggling to think of something that wouldn't be noticed straight away by the ECU and result in a fault code.
Don't suppose the exhaust / cat is blocked? It did blow an air injection pipe?
Then again, I would have thought that would strangle it progressively more at higher revs.
Has the battery been disconnected recently? Maybe the ECU is "re-learning" the correct idle speed and ignition advance. It shouldn't be taking this long though - unless it's not getting its' permanent feed from the battery to keep the non volatile RAM safe? No fuses blown?
Is the air injection pipe sealed now? I guess air being sucked into the pipe could fool the lambda sensors into thinking it's got a lean mixture and result in it running too rich? Then again closed loop won't be active during idle and it'd probably result in a fault light. I take it the engine and emissions fault lights do work OK?
It's a real tough one!
Kevin