I don't see it mentioned yet - but have you taken the time out to probe any of the connectors that go to any of the most common engine sensors to see if those are within spec per factory guidelines? It's possible that 1 or more connectors coudl have bad internal wires under the wire wrap - or broken wires, which would lead to malfunctioning sensors and/or engine issues.
Also, have you probed each of your sensors with a multimeter to see what their output specs are also?
I know you have stated that you replaced or cleaned your ICV - what is the output of it when probed, does it match the factory specs? If it is reading under or over the factory specs, it's going to cause idle control issues when cold, when hot, when at idle or when driving.
I too was having cold start issues. I probed my ICV and it was well below the specs per what the factory readings should be for that part. I then soaked it in carb/brake cleaner, let it dry - tapped it with a small hammer all around the exterior casing, then reinstalled and probed it again. This time around, the "hum" or "buzz" from the ICV when powered up was much stronger and the specs were within what the factory specs should be once probed. When starting the car from a bone cold start - no more problems starting it and no more issues with drivability as the engine was warming up.
Even if the ICV is new, is a used replacement, etc - I would still spec it out with a multimeter and post up your results. Also as I said above, I would start probing out the actual connectors that go to the engine sensors - it's quite possible either one or more are not connected 100% or there is damage to the actual wires in the casing.