At the moment I only have a 2002 reference manual. Therefore, some of the wiring colors may be different.
The two speed fan has (3) wires. The black is the ground. OG/LB is the high speed and RD/OG is the low speed.
A basic fan test is to use a jumpper wire from the battery directly to the fan. One wire from the black to ground. +12 volts to each fan speed terminal. There should be a clear difference in fan speed.
The fact that the black wire through the connector show signs of overheating should be looked into. This could be the results of dirt/grease in the connector. Clean with contact cleaner and re-grease with silcone di-electric grease (same kind used on spark plugs).
The connector may be beyond repair. The fan uses a lot of current therefore, the connector needs to be able to carry it without overheating. A connector replacement may be needed.
This could also be a frame ground problem. Check the battery. Is it clean? Are the terminals clean and tight? What about the frame ground connectors around the battery?
Seams plausible to me that the same thing has caused both fans to fail. However, it could be just plain old bad luck.
What if the low speed and high speed fan is engaging at the same time? I honestly do not know if this could happen. To test, check for +12 volts at the fan harness. Voltage should be present on only one lead at a time.
If there is voltage on both leads, we need to test/replace the CCRM.
OBTW, it may have taken 2 weeks before enough heat built up to actually melt and damage the connnector.