Ok, so a few things....I operate and manage a family owned auto parts store, so lets go thru the basics....
If it was a coil, it wouldn't run good at 2K RPM. Coils either work or they don't...the only in between is when they have an internal short and randomly misfire all the time or quit working when it gets hot, in this case, it's most likely not the culprit. We have one, but haven't sold many to local shops.
If it was the distributor pickup, it wouldn't run at all. It either works or it don't. We have one, but haven't sold many.
If it was the crank position sensor, it wouldn't run at all. We have one, but haven't sold many.
If it was the MAP sensor (it has one), the symptoms above are the general case. If the sensor can't read a higher vacuum reading to let the motor know it's not under a load (idle), it may tell the computer it has a lower vacuum (load) and will confuse the computer because it associates manifold pressure with throttle position and RPM. Sometimes the sensor won't fail enough in the parameter swing reading to throw a code. Very likely this may be your issue. We have 3 and have sold many (62) last year alone.
If it was the IAC (idle air control), it would not be able to retain a constant idle. If the idle goes up to 2k upon startup and comes back down on it's own, that means it's working. That doesn't mean it's working accurately as the pintle inside it can give false readings to the computer, but this will not cause it to hiccup and carry on running bad. Have one, but haven't sold one in 18 months.
If it was the TPS (throttle position sensor), it can cause similar symptoms. Keep in mind that the idle position is used frequently and the sensor may wear the contacts at that position and give the computer random inputs and cause an erratic idle or even a runability issue like you have. This sensor is like a MAP sensor...it could not fail enough for the computer to throw a code. Very possible this is your issue as well. Have several of these and sold 54 of these last year.
Fuel pressure can cause similar issues. If you can drive it on the street and it runs good under a load, then it's not your fuel pressure or a fuel filter issue.
Check all visible grounds under the hood for loose connections. If your able to get to it easily, then loosen the bolt and retighten.
Have a genuine shop that has a nice computer that can see the parameters of individual sensors. The ones oreally and nappy auto parts have only read codes.
Good luck and keep us posted!
~Joe