I have been so nervous for the last 7 hours while I haven't been able to get to the internet that someone would correct me in the video before I had a chance to salvage some shred of dignity. The line with melted insulation in the video that I say is the kickdown cable is obviously NOT the kickdown cable as it goes into the transfer case

. It is the speedo cable. Whew, now that we got that out of the way...
Apparently, AAA was having a hard time tracking down a tow truck that would tow it this time around because it is too big to tow safely. A service guy came over and we took a look at everything. After taking a look at it, the seal is obviously what caught our eye. We figured that it was oil from the tcase that was originally burning and not atf. We pushed the seal back in and drove it 7 miles to a transmission shop. He followed me with his fire extinguisher at the ready. We made it without any issues.
The tranny guy (teehee) is going to take the xfer case and transmission down and inspect everything for free and chat with me in the morning. The guy was awesome though. He took nearly 30 minutes to chat with me about stuff and show me various things in his shop to illustrate what he was talking about. We talked about trans coolers and he is all about mounting them through the radiator, which I am pretty sure is a huge no-no. He said they do it all the time (for years and years) and never have issues.
I thought it was interesting when he was saying the coolers work better when you do not mount it in series with the internal radiator cooler. He said that in series makes the temperatures slightly lower, but at a cost of greatly reduced flow with a net effect of less effective transmission cooling. He also pointed out that the oil cools and lubricates (the planetaries) and if the flow is low and the planetaries aren't getting enough lubrication that it runs even hotter. Seems to make sense.
I am thinking the xfer case got too hot due to a number of factors. First, the transmission was likely quite hot and transferring a fair amount of heat to the xfer case. Second, my mufflers run right next to the xfer case (the muffler guys said years ago that it wouldn't be a problem, and it hasn't been, until now) and don't have a heat shield... but they will. Third, I guess I am an idiot and have totally neglected my xfer case - I had no idea it was something that needed to be checked like transmission fluid and engine oil. I am not saying it was low or anything, I just have never paid attention to it. I have had some liquid slowly saturating my cross member right under it, but I always assumed it was ATF (not enough to drip and puddle, just enough to keep it wet). In retrospect, it could have easily been oil from the tcase.
The transmission and xfer case are the last part of my driveline to have been replaced under my ownership, so this will give me pretty good peace of mind once I am beyond it.