We have a floor!
So the guys we had come finish the floor were amazing. They got here at 8am on Tuesday and worked until 6:30pm. They were back in the morning to finish up grouting and were out by lunch time. The amount they were able to do while I was in the shower before leaving for work was more than what Mr. Handy and I got done in an hour. It's pretty humbling to see people work 500% faster than you can and not even look tired.
Mr. Handy works from home so he kept me updated while I was at work. They were wrapping up when I got home, but they managed to get the entire room tiled and ready for grouting in the morning. When I got home the next day they had everything finished, grouted, and cleaned up.
We have a floor! We have a room! We just need to add the doors back to close off this side of the basement and add trim to the ceiling and floor.
Materials:
Underlayment: Ditra Heat Duo
Unmodified thinset for under Ditra: Mapei Kerabond
Unmodified thinset for over Ditra for large tile: Mapei Kerabond T
Grout: Mapei Ultracolor Plus FA in Bahama Beige (this grout doesn't need a sealant and is stain resistant)