Good, you have done all the basic stuff. Now to find the real problem. The warm wire may be a good starting point.
Over-all the size and quality of the wiring on these tractors is less than ideal. Most all of the wires are too small and the crimped on terminals, especially the flat female ends are of poor quality. What I find is that the metal is not strong enough to maintain the pinching pressure needed to hold onto the male end. The curls on the female side loose their grip with vibration and eventually cause problems. You can squeeze then down with pliers but they only hold for a while. Eventually one of the curls will break off.
If I remember correctly the regulator senses system (battery) voltage through the fuse box, which is powered through the key switch. Then it sends voltage to the alternator to "excite" the field coil. This then raises the output voltage which goes through the ammeter, to the starter connection and back to the battery.
I don't think there is a great deal of current that flows from the regulator to the alternator but a bad wire/connection could certainly lower the voltage that is actually seen at the alternator. You should be able to use an ohmmeter to measure the resistance of that wire between the regulator and the alternator. Be sure to remove both ends to insure you are not reading some other part of the circuit. Or you could always make up a temporary jumper wire to bypass the wire in the harness to go directly between the alternator and the regulator. Also don't forget that the regulator needs a good clean ground for proper voltage reference.
The same three electrical rules apply to trailers and tractors:
Check your grounds
Check your grounds
Check your grounds ~ Francis Robinson aka: Farmer
Thinking about the whole thing, it is probably much more common for the regulator to fail than the alternator. I fought the bad terminal/small wire thing on my 284 for quite some time and eventually the regulator failed. A replacement was half the cost of a re-man Delco alternator that put out way more amps and had an internal regulator. The down side of that conversion is that the Delco was not a totally enclosed fan design so on the rare occasion that I am working in dusty conditions I have to be vigilant about blowing the dirt out of the alternator.
The key switch could play a minor role in this but if you put it in run and get full battery voltage at the fuses, the switch is probably fine. The most common failure mode of the key switch is the glow plug circuit is fully fed through the switch contacts. That puts a 30A load on the switch and can burn the contacts. Also the glow plug wire is too small. The best solution for that is to install a solenoid so that only the relay current goes through the switch and full plug current comes from the battery directly (through the solenoid).