First I want to say that I have read most of this thred and I am not "bashing" anyone or anything so if I go over ground that has been covered I apologize.
The stepper motor is controlled by a table called IAC Warmup Steps and is influenced by the Vehicle Speed Sensor. If the hot idle stepper count is not between 30 and 45 and the values in this software table are not close, when you come to a stop the IAC stepper motor drives to the software value first and then tries to get to the programmed idle speed. So if the stepper motor drives to a software value of 20 for example but in reality your bike idles at 45 steps then the stepper motor over drives and then has to catch itself back to 45. While it is catching itself the bike will not idle quite right or feel like it is stumbling. Most Harley dealers will say you do not need to adjust the throttle stop, but if the hot idle stepper count is way off then there is a limit to where you can program the software. For example I had a 2003 FFUltra bike in a couple of weeks ago and the idle was pretty irratic, the hot idle stepper count was at 65. You can not adjust the software that high as it has limits, so it was always stumbling and searching. This bike had pretty high mileage and the stop had never been adjusted. All those miles of banging the throttle stop had made the throttle blade more closed which means the stepper motor has to be more open to idle. I adjusted the stepper counts with the throttle stop screw and watching the stepper counts in my software program. Once I was at say around 35-40 counts, I put all of the backing plate and assembly back together. Restarted the bike and it would idle stable and when I would decel down on the dyno it would idle at 1050rpm or so until the VSS was at zero then the stepper motor would take over and the idle would drop to the programmed idle speed of 1000rpm. The stepper motor will not work until the VSS(Vehicle Speed Sensor) is at zero and this is when the stepper motor takes over to idle the bike at 1000rpm or some say closed loop idle control. All of the Delphi cable bikes have this same table and adjustment. In 2007 Harley decided to make the throttle stop adjustment a special 5-point security bit which is kind of hard to find.
The only way to fix this is to get into the ECU and adjust the IAC software table and adjust the throttle blade so they are within a reasonable range of each other. Meaning hot idle live stepper count is (30-45)close to the programmed stepper count. The only way to do this would be Digital Tech and the Harley dealers around here will not do it or say you do not need to do it. There are aftermarket diagnostic software programs like Daytona Twin Tec Twin Scan 2 or Technoresearch VDSTS that would allow the adjustment of the throttle stop but you would not know exactly what the programmed software IAC values are in the ECU. The other option is to use any of the tuning software packages like TTS, Direct Link, SERT or SEST as they all have this IAC software table and they all have diagnostic capability to read the strepper counts so they can be adjusted. This would allow the software and IAC to be closely matched.
All of this assumes you do have an intake that is not leaking which if it is the stepper counts will be very low or at zero.
If you are running a piggy back fuel controller you have no way of knowing what the hot idle IAC reading is live and you have no way of knowing what the programmed value is in the ECU.
This system also works for cold start, all Harleys will idle up on startup and going to 1500-1800 on first start is not a bad thing. Go start any modern efi automobile and see what it does. This stepper motor now controls engine rpm versus heat so a bike that is operating correctly on first start will flare to say 1600rpm then idle down to 1300, then 1200, and once the motor has some heat in it say around 180-200F the idle will be at 1000rpm or the programmed idle rpm. This is assuming that the bike has the correct fuel at idle too lean and it may not idle correctly and too rich and it will "blubber". Another table involved with first cold start is Warmup Enrichment which will add fuel until a certain temp or time is reached. The colder the bike more fuel is added and the warmer the bike less fuel is added.
DBW bikes do not have a stepper motor so they use throttle balde control for closed loop idle. There is still a software table that can be adjusted to match Step counts both software and real time. It is a little confusing but it does do the same thing only does not have a stepper motor. Most DBW bikes when hot will show a real IAC count of 45-50 and it is pretty stable.
Hope this helps some?