Do you still have the basic scenario problem: okay when warming up...not okay when warmed up ?
About the IAC valve:
that little "door" only moves enough to be able to completely
close and open the little opening. So when you turned it with your hand, were you able to completely turn the valve such that the opening was fully closed and opened by the door? Or did you feel resistance and were not able to fully close/open the door with your hand ?
As the factory service manual says:
When I cleaned my IAC valve, I also used a 9 Volt battery...but it barely moved the little "door" (maybe I got unlucky and had a drained 9V battery), but I hooked up two wires to the car battery. I used the car battery instead of the 9V battery. For my situation, the little IAC door did NOT close all the way. I verified that there was no blockage or debris inside the opening and around the door... So I loosened the two little screws holding the thermostatic spring housing and slightly turned the housing with the screws and re-tightened. Re-did the battery test and verified that the door fully opened and fully closed when the wires were hooked up the two different ways. Which way you have to turn it, it depends...I don't remember which way I turned the spring housing. You can see the screws on the left side of the IAC assembly (by the fingers in the photo below):
That was my scenario...on this forum most people don't mess with those two screws holding the spring housing...people just clean everything and they're good to go!
So I am just telling you this info to keep in mind...
Make sure that the rubber "frog" gasket between the IAC assembly and the throttle body is installed/seated properly and that the 3 hoses (2 coolant and 1 air) are connected in the proper location.
If you have the original ECT sensor, I would highly recommend to change it, even if it seems to be okay. An ECT that is going bad will cause all sorts of problems...so might as well be safe and replace it. It's not expensive and it's really easy to replace.
I am sure more experienced users will provide more info...
EDIT: Oh, and the TVV controls air/vacuum to the vapor canister for fuel vapor based upon if the engine is cold or hot. If this branch is not operating properly, idle/stalling issues might arise. On 1996 and newer, the 4 cyl. i don't think has the TVV anymore...instead it's a vacuum switch. I have a 1996 4 cyl with an electric vacuum switch (hence why you don't see it on my engine...in the photo I posted)