Hi Ryan. Is the p0340 an active code? It may be the source of the high idle.
Also, check the coolant level in the radiator. Low coolant levels may make idle go high as the engine is trying to get coolant to the ECT sensor. If the coolant level goes far enough low the sensor has no coolant to measure. The gauge might even read normal. Just want you to beware of that. And, we need to get you a good reservoir lid pronto. I will keep an eye out if I get up to Rayrays.
As far as the voltage reading from the alternator, it will only be above the battery voltage by so much. The battery voltage "excites" the alternator. I was seeing a range of 13.6 to 14.3 depending on the circumstances-thought the alternator was bad, stuck in another and got the same readings. I put the "old" alternator in a box for a spare.
Then, a few months later the battery went-5 years and 1 week to the date of buying it from wally world. T
Now with the new battery I see readings from 13.9 to 14.3
See if cleaning the battery posts help with the charge level. These trucks are real picky about having clean battery terminals. I always used to grease or lube battery posts to prevent corrosion, but you can't do that to these explorers by golly.