FYI, in case you didn't already know, the ATC is sold separately, in case the differential is good and you don't want to replace the whole assembly. 

As far as I know, A/C systems on Ford vehicles come with the dye already inside the system from the factory. So leaks can be detected faster.    This is from the 2015 Service Manual, but I would expect it to still be the same.  Fluorescent Dye Leak Detection.pdf

Pulled the plug, made no difference other than throwing an AWD malfunction error.

Yeah, I unplugged it, threw an error on the dash, but didn't change anything as far as driving. Wheels acted like trying to grab on pavement when turning... as if it's in a 4WD in 4WD. 

This probably indicates a bad (Active Torque Coupling (ATC) solenoid.  This is the front part of the RDU and controls how much the rear axle connects with the front.

I was leaning towards this answer.   It could be the valve, but it may also be a small, very slow leak that you will never find on your own.  The only way to find the leak itself is to perform a dye test, where they inject a dye into the A/C system.  The leak will show under ultraviolet light.   Sometimes the seals dry out causing the leak over time, eventually resulting in total cooling failure ( No A/C ) due to complete loss of refrigerant.   I had very similar symptoms on a couple of different brand cars over the years.  Acted just as you initially described.  It was a leak.

There are plenty of pictures of the installed CVF front mount intercooler  ( FMIC ), and install instructions on-line.  You just have to do a search.   As far as performance gains, the purpose of the FMIC is not for a performance gain, not directly.  The purpose of the FMIC is to keep the charge temp into the intake cooler, for a longer period of time.  If you want performance gains, then there are multiple " bolt-on "pathways to get there.   1. Performance Tune   2. Larger Turbos   3. Increased Fuel Flow   4. Larger Exhaust   Some of the above options require for them to be used together  

Much of this issue could also be attributed to a low refrigerant level.  As the car runs a while and gets hot, the refrigerant expands as it heats and can work better.  It certainly could be the valve, but buying a refrigerant pressure gauge at an auto parts store and checking the level/pressure while its running could rule this out.  Even without a major leak, refrigerant levels do drop due to evaporation through the hoses and tiny leaks at the fill valves on the high and low pressure side.  If it is low, adding some gas could get you 5 plus more years without a problem.  

I disabled traction control through dash settings. I may try your suggestion on unplugging the connector if I can access it.

Welcome.   With a used PTU installed clouds the diagnostics.   I suggest you electrically disconnect the RDU coupler and test drive it like that. What method did you use?   I can get onto the interstate and depending on how hard I accelerate the power to the rear will stay on up to around 60mph.