Not looking to get into the whole idle control topic here, but a few suggested approaches that may help in project development. Tuning vs advance vs air. First runs typically use no IAC air, and the engine is made to run with throttle until warmed. Then, the idle tuning results in the throttle stop setting for a warm stable idle at a reasonably stable target rpm. All good so far, and the engine is running stable at fueling for peak-torque and stability (e.g., minimum MAP).
Next is warm re-start tuning, finding warm priming pulse with zero or very low ASE and WUE for quick and reliable warm restarts. Good. From there we can alter fueling for colder conditions, using our previous tuning as the baseline, adding fuel, air or timing in order to maintain the target Lambda/AFR for stable operation during warmup. OK, as some engines typically need a little more help with cold-start stability than going straight to warm idle rpm target with more fuel.
Air versus advance. Air is slow to react and I view it as a general idle speed
range correction, bringing idle to the neighborhood it should be when conditions or loads change substantially (temperature, altitude, fuel change, whatever that is relatively slow). Conversely, idle timing advance is very fast response, but can be limited in its correction authority. So, stable tuning with timing advance to maintain target, and added air if it's needed to get there.
Depending on the engine, with common load changes and other conditions, the air can be simply set by throttle stop as carburetors were (step 1 above). This is all that's needed with many or even most engines, and works especially well for larger or well-tuned engines. All good. For cold warmup, cold advance timing can be added, but this often isn't enough stability and air can be added - if necessary - with an on/off valve, cable lever, or open-loop steps, etc. As-above, air is added to again bring it into the general area, where timing can quickly push or pull it to specific target rpm.
I hope you can see the incremental development of the idle controls, as the engine shows demand for each. Tune it well for warm stability, then use timing for quick and smaller corrections, and air for larger, slower corrections to bring it into the timing correction range. I hope that helps.