Jumping in on this discussion as I've been working a similar issue for about a year.. I've finally made some headway, but it definitely seems that some of the issue here are unrelated and unique to each rig.. But nevertheless, here's my story..
I bought the van used from Ford dealer, in October 2020 (it's a 2018 T350 3.7L) it had about 50k miles on it.. AC worked fine until about late August 2021.. Started blowing warm in some vents, cold in others.. Tried to struggle through the last 5-6 weeks of heat (in Southern Oregon).. I found I could run the AC and get cold air as long as I didn't go above a 2 on the dial, also hopping on the freeway seemed to provide enough cooling that the AC then could be turned to max.. Thought condenser fan was the culprit, but after testing of the fan, we found no faults.. managed with it until the Fall took to shop, they checked AC charge, noticed the High side pressure was high, thought maybe overcharged so recirculated the system.. seemed to work, pressure looked nominal but ambient temperatures had dropped with the weather so, didn't know for sure.. Fast forward Summer 2022 and we're back to trying to manage by not turning the AC above 2... Pretty soon, that didn't work either. I had nothing at all.. decided to replace the condenser fan since we could get cold air under certain very specific circumstances, like going through the carwash, the AC would blow ice cold, pull out and then it would quit..etc.. Replaced the fan assembly, the AC worked.. but then we noticed, the fan wouldn't kick in to high speed, or at least wouldn't stay on.. immediately the compressor would start cycling on and off.. So, we decided to move some fan relays around.. Put the low speed fan relay to the High speed location.. voila.. the fan stopped turning off and the AC stayed cold.. Not sure the exact function with the low speed, since it must have a bad relay in it currently.. though it's still working.. Gonna replace it FORD # for Hi speed & Low speed Relays ( 5M5T-14B192-EA ) found aftermarket equivalent HELLA brand # 933332531 at local parts store.. gonna try it out.. The only problem I'm still having, is that when I turn the "Rear-Air" on, it shuts the compressor down.. going back into the shop to check refrigerant level, pressures, and see what circuits/parameters the Climate control system is using to make it's decisions.. Hope this helps some of you, check those relays.. I read about them some time back and ignored it.. They were definitely part of the problem.. Hopefully update soon about the rear issues and how that's resolved.