I'm posting my experience with this in case someone else has the same problem with their JD 3720 cab AC.
If you have mouse smell coming out of the cab AC, the only way to fix it is to remove the roof of the cab so you can have access to the evaporator, fan motors, and every place where mouse detritus may be in the air flow.
I highly recommend you do this in a covered work area. The job may take longer than you expect, and it's nice to work in the shade.
Removing the roof
Thirteen bolts hold the roof on. They are easy to access and remove. Two of them require you to remove the two rear lights to get to them. Each light is held on with two bolts, and its wiring harness has a simple snap connector.
After the bolts were out, my roof was slightly stuck, but it came free with bit of encouragement from a small pry bar. I started at the back and worked gradually around the cab until the roof was not stuck anywhere. Doing this did not damage the seal.
To remove the roof, you want to lift straight up. The roof has 13 bolts integrated into it that stick down, and you want to prevent them from tearing up the seal. It takes two people to do this safely, and you will each need a stable step ladder.
I was lucky because I had a winch and pulley that I had rigged up before to assist in loading a cargo carrier on my car roof. I ran an adjustable strap across the cab roof and placed its hook ends under the edges of the roof. The winch cable hook went under the middle of the strap.
While my wife cranked the winch, I easily guided the roof bolts out of their holes. I found that the roof balanced perfectly if the strap was just a few inches back of center. With the roof in the air, I backed the tractor out and lowered the roof to the ground. The winch was even handier when I replaced the roof. It allowed me to to guide the bolts into their holes without damaging the seal.
Cleaning out the mess
First I started with a shop vac. The cab has an inside roof structure that you can set a shop vac on. I scraped and vacuumed up as much detritus as I could. I also used a computer vacuum kit, which attaches to a regular vacuum hose but necks down to a smaller hose and cleaning tools. This let me reach into narrow places and crevices.
Then I used high pressure air to blow out areas I couldn't get with the vacuum. I wore a dust mask and goggles and was glad that I did.
Now came the difficult part. There was no way to get to the evaporator drip pan, and it was an especially dirty area. It needed a good flushing out, and so did everything else up there if I wanted to really fix the smell problem. But right behind the drip pan, on both sides and less than an inch above it, were the two large return air vents that open into the cab. The system is designed to handle the drips from the evaporator coil, not the amount of water needed for a proper flushing.
My solution. I went inside the cab and removed the two plastic return air grills and their foam filters at the back top of the cab. I could then pull back the headliner enough to stuff towels inside the return air openings. I went back on top and pulled the towels up and stuffed them back down until I was sure I had the openings blocked. Inside the cab, the two towels hung down like giant wicks. As a extra measure, I put two buckets below them. The tractor seat arms did a good job of holding the buckets in place.
Now I was able to move the tractor outside and use my pressure washer to clean the evaporator coil, drip pan, and all the surrounding areas that were contaminated. My wife kept watch inside the cab to stop me in case the towel system got overloaded. It worked. I think a steam cleaner might be a better option for this job, but I didn't have one, and I did have a pressure washer.
Next, I used a foaming AC coil solvent on the evaporator, the non toxic kind, designed for this purpose. And followed that with another pressure washer rinse. This left the evaporator coils and fins nice and clean, maximizing the AC system's ability to cool.
Then a final shop vac go over, sucking up as much of rinse water as possible from all areas. I didn't want to leave any dissolved solids to dry and be a source of odor.
Extras
Since I had the top down, I could check all the wiring. I did find one wire where the insulation had been chewed off by the mice. I taped it up.
And, probably more symbolic than practical, I sprayed some air freshener on the evaporator before replacing the roof.
I decided it was also the time to spring for a new AC air filter.
Replacing the roof
As I said before, I had a winch and pulley system to make the job really easy for me. The goal is to get the bolts to drop into their holes without dragging them across the roof seal enough to tear it up. If the seal is broken, replace it. The air flow system for heating and cooling depends on it to work properly.
After the roof is in place, you need to push it down all around so the bolts will reach far enough to start the nuts. I replaced the nuts in two stages. I started them manually, and then went back with a cordless screwdriver to tighten them up. When starting them manually, I still used my socket extensions, but I turned them by hand, like a handleless screwdriver. This worked well, especially when I couldn't see what I was doing and had to go by feel.
Prevention
How to keep this from happening again? My homestead is surrounded by wild habitat and teems with mice. I don't have a proper structure to keep the tractor in. I've tried using mouse traps in the cab, and that catches mice like crazy, but it's too hard to maintain. Also, it finally struck me as silly to be setting up something that would lure mice into the cab. I don't like poison because of its unknown downstream effect on the local food chain. For example, my beloved dog spends a lot of time outdoors hunting mice.
The local JD dealer recommended some Fresh Cab botanical rodent repellent. It contains Balsam Fir Oil and doesn't smell too bad. I'm going to try it this winter.
Thank all of you for your help and suggestions.
Michael