With an unstable idle like that and revs going up to 1,500 then down to a stall, there are only a few thoughts in my mind. You also need to start using the OBD system to help rule out a few possibilities:

a) The ECU doesn't even know it's supposed to be maintaining idle. This would by far be my #1 suspicion based on some of the things you've said. The TPS switch is either incorrectly adjusted, is faulty or the throttle plate is binding in the throat. This needs be verified using a strip of 24 bond paper as a spacer at the throttle plate stop screw, both to get a click and then to verify it with a meter. Double check that the throttle plate isn't binding (force it closed by jand to see if that helps), the throat is clean (especially around the edge of the plate, requiring the air supply tube to be removed) and that the TPS electrical connector is firmly seated. Much better and even simpler than using a meter to verify TPS operation and adjustment is to get the ECU to tell you if it can see the switch opening and closing. You should use the OBD system to verify this using DTM 2 on port 2 (as described here in the FAQ).

b) The ECU can't maintain idle. This would normally suggest a dirty/worn/sticky idle air valve or a loose connector. You said you replaced the IAC controller. I'm not sure what you mean by that. Again, use the OBD system to verify operation of the IAC using DTM 3 on port 2 (as in the FAQ).

c) The IAC can only adjust idle when the throttle plate is sufficiently closed when at rest. If the throttle plate is binding or there's even the remotest chance someone has ever played with the idle stop screw, the turnbuckle linkage rod or throttle cable then you need to disconnect/loosen and readjust everything, including the TPS, using the 1/4 turn method for the idle stop screw and 24 bond paper to adjust for the TPS click, making sure when you later connect it that there's a bit of slack in both the linkage rod and the throttle cable when the throttle is closed. All that should be in the FAQ.

d) There's an incorrect sensor signal, specifically the block temp sensor. Normally when this happens the idle goes high as it warms up and stays high, not going back down again. Still, I'd want to verify the ohms on both a cold and warm block. Resistance values can be found if you do a bit of searching here and elsewhere.

e) There's uncontrolled air getting into the throttle plate bypass air supply -the two hoses on the IAC. Check carefully for splits in those hoses, especially the one that goes to the throttle body.

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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now