Well, here's the follow-up. I've been pretty busy at work during the day, so I've not been afforded the chance to call Rick at Rick's Motorsports. (I wear a lot of different hats at work, so I stay pretty busy) I did, however, have a half hour on Friday to buy a few butt connectors for 14-16 gauge wire so I could splice the stator wires directly to the wires going to the R/R. So far, so good. I've ridden a little bit here and there and each time I stopped, I pulled the seat off and felt the wires. They're not even getting hot now.

I pulled the maintenance manual out and checked out the wiring schematic in the back to make sure there's nothing else these three wires go to, and sure enough, they go straight from the stator to the R/R, so I was less worried about splicing the wires and having something get damaged as a result.

I'm going to assume this was a result of a situation that scutfargas mentioned happened to him where the stator plug wasn't connected securely enough to the female connector from the R/R, causing arcing and heating up of the wires enough to melt the plastic connector plug. It was as far in as I could get it, but I guess it may not have been far enough.