Here a few pix of the soldered, shrink wrapped and loomed fix ... only took about an hour which also included brushing down the dirt from the top of the differential and surrounding area first, so it wouldn't fall in my eyes while working underneath and upside down. If I had actually PLANNED on doing this, instead of just spuriously doing it, then I would have pressure washed underneath the car the day before, and let it dry overnight, but my quick approach with a brush and air compressor mostly worked and I surprisingly didn't get any dirt in my eyes.
When I was cutting off the damaged portion, I deliberately left the OEM wiring longer then necessary, so that it hung down PAST the top of differential. That way it was easier to solder the aftermarket pigtail to it. I also offset the splice joints so that both wires would still fit into the wire loom even after shrink wrapping them. Then, after shrink wrapping and tucking the wires back into the OEM wire loom, I simply added an extra piece of loom to make up for the extra wire length. I also used secret electrical tape tricks in order to securely attach the end of the loom to the locking connector itself, rather then stopping short of it (like the OEM connector had). This should prevent the new wire from fatiguing again, while still allowing for the new connector's locking function to work properly.
Overall, I think the repair came out good.
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