This time I didn't speak to Ulfric, but instead I bought the house, visited the house, then returned to the steward to buy the upgrades. My problem was solved and the situation inside my home was taken care of.
However.. Now when I speak to Ulfric, I'm not given the dialogue option that begins/completes the "Thane of Eastmarch" quest. I was excited that the previous situation was resolved and I've already written over my earlier save, so reloading isn't an option. I've googled the crap out of my issue and I can't find any reports of this particular bug. I've tried resetting and re-completing both "Blood on the Ice" and "Liberation of Skyrim" in hopes that I'd be given the option to become thane, but to no avail.
Does anyone have any suggestions as to how I can correct this? Is there a console command that will set me as the thane of Windhelm and place the housecarl in my home?
If it makes any difference, one thing I did differently before I bought the house the second time was I exploited the console and I used "coc WindhelmPalaceoftheKings" to quickly move 2,000 lbs. of equipment from my previous house to Windhelm.