OK, good feedback.

The IAC's resistance should be between 6-10 ohms & is test lead polarity sensitive. as I noted above.
Are the ones your measuring Motorcraft IAC's, or some afermarket brand?????

Your right about the battery, if it's KOEO reading is 10.5-11.0 volts it's discharged & either needs to be recharged, or replaced.

Low battery voltage can cause all sorts of mischief on computer controlled vehicles, so I'd address this BEFORE beginning to throw parts at the problem.

Either have the battery recharged & load tested, or replace it.

Once you get that squared away, do a idle relearn for the computer. I use the abbreviated one called out for my 94 Taurus & it works fine for my 99 4.0L Ranger.

Start the engine cold & let it idle down some, then shift into ALL gears, including "R", then let it idle, undriven, until it fully warms up on the temp gauge, then shift into ALL the gears again.

This will have the computer quickly relearn it's it's cold & warm start, idle strategy.

The remainder of what it needs to relearn it can do while driving over time.

If your experiencing other than idle driveability problems, you can go through Fords specific relearn sequence, which takes a little more time on the road & requires specific accelleration runs & braking sequences, ect, to have the computer learn all the remainder of what it needs to remember.

So I'd address the known battery problem first, then do the idle relearn & see how it may be affecting the idle speed anomaly.

If there is no change, then have the computer scanned for "pending" trouble codes that might be stored, but not matured to the point of turining the CEL trouble light on, as they may offer up some good troubleshooting clues.

If you don't have a scantool, or code reader, most autoparts stores nowdays will scan the computer at no cost, if your having poblems, even if the CEL is off. Some won't pull codes, unless the CEL is on, so you could just pull the IAC connector to turn the CEL on (wink, wink), then go get the codes scanned. "Any port in a storm" RIGHT!!!! lol

If the trouble code scan provides naught, then inspect more carefully for a vacuum leak somewhere. This could range from the Heater/AC controls, to the vapor recovery system, to a gummed up/stuck open PCV valve, to leaky intake manafold gaskets.
In fact if the PCV valve is due, or past due for change, replace it.

Any of these things can upset the IAC's idle air bleed balance & confuse the computer.

A dirty MAF sensor can muddy the waters too!!!!

Just some more troubleshooting thoughts for pondering.
Let us know how it goes.