I think I'm close to being an "experienced" John Deere 3720 Air Conditioning trouble shooter (with a lot of help from the dealer). Problem solved.
What did I learn? After finding the high side pressure "kicking" out the compressor at about 350 PSI, I changed the expansion valve (which meant removing the cab roof) and the dryer in front. This didn't help....but put me one step closer to solving the problem......compressor or evaporator coil (up in the cab roof). So, instead of going it alone, I called our local dealer and their air conditioning expert came out to the farm (which was a 100 degree day in Wisconsin). He trouble shot the A/C system for 2 hours and found nothing wrong.....EXCEPT......behind the battery and turbo cooler (which none of us can see or clean)....was COMPLETELY PLUGGED!!!! We took our pressure washer and completely cleaned it out, blew it dry, and fired it up.......47 degrees coming out the vents!!!!
I asked the gentlemen how this could affect the system, he stated "It's a bad design...very little room for ANY inefficiency in the way the system cools down the high side". Which I stated...."It's a farm tractor......aren't these things meant to be loaded with dust and dirt and keep on chugging?".......which he replied..."exactly".
So, removing the battery, taking the two hold down bolts on the turbo cooler out (leaving it attached via the two hoses) and pressure washing.....is the answer in my case. Though, after reading many threads on this topic.......keeping the condenser clean along with the back filter is the key.......it's getting to it that takes time and effort.