So I did burp it again, but the problem persisted.
After doing some reading, I don’t think I have been properly burping. On my next try, I will do the following things, which you intelligent and patient people probably assumed I was doing in the first place:
-incline the car on a slope
-wait for the thermostat to cycle a few times, perhaps as long as 30 or 40 minutes (probably unnecessary, but I may as well just to make sure.)
The next step is to check the IPS (idle position sensor). It is part of the TPS (throttle position sensor) and is a simple switch that tells the computer that you have taken your foot off the gas and it is supposed to control the idle.
I don’t have a tech manual for your particular vehicle but generally you will have two 3 pin connectors to the TPS. Remove both and if you take an ohm meter and put it across the middle and one outer pin, operate the throttle and the resistance varies, that is the TPS. If you get a short when the throttle is closed the becomes an open when the throttle is moved, or is open but shows a short at WOT (wide open throttle) that is the IPS. Middle to one outer pin is the WOT position, middle to the other outer pin is the idle position.
If you are not getting the idle position, then you need to either replace or adjust the TPS.
You may have already mentioned this OP, but have you followed the manufacturer’s procedure to set the engine idle rpm? Have you made sure the throttle cable isn’t binding and has the proper free play? And measured the idle rpm with the air control valve electrical connector disconnected? It probably should be a around 600 - 650, double check the specs I mention here, just estimates, the factory service data is what you need. If the base-line idle is out of spec, adjust the idle speed screw. Then after the baseline idle rpm is set, with the air control valve re-connected, the idle speed should probably be around 750 rpm with no engine load, and 800 rpm if the AC, headlights etc are on.