So, I've had a couple of great days! Today, my son came over and we fixed the Jeep! We removed the transmission top cover and got the shift rails moving. Then we got the transmission in neutral We drained all the sludge, put a couple quarts of diesel fuel in the case and sloshed it around by rocking the Jeep side to side. We let the diesel sit for an hour while we went and got some GL4 90W. Drained the diesel fuel and refilled with GL4. Took her for a drive and all went well. I'll do another drain/fill in a while--there was definitely some rust inside. But she's fixed! Thank you all for your help!
And...2 days ago, my oncologist told me that, as of now, I'm cancer free! There will be future testing, and I still need an operation, but I've moved from the treatment stage to the surveillance stage! Happy Days!
Forgot to add...the transfer case oil was good!