If you are looking for a nice frame you can get my attainable dream bike:
https://www.rencycles.com/yarak.
You could customize it as needed as well and still be pretty reasonable for handmade titanium in the U.S. by someone who knows their stuff.
When I thought of a titanium fixed gear bike, this was more or less what I pictured where as a lot of other stuff just seems off or has stuff I can't get down with the sickness on.