NY to LA is 45-50 hours, if you drive constantly. Take 6 days, and drive 6-8 hours a day, realistically.
I tow a 5000lb Tradewind with a 1/2 ton Vortec 5.7/3:73 Suburban. Works very well.
Towing mileage is around 12mpg, sometimes a little better. Solo mileage is between 14.5 and 18mpg city/highway. Paid $12k for the Suburban with 60kMiles on it.
Average combination mileage city/highway is about 15.5
I am yet to encounter a grade or mountain that gave me problems, but I have never towed at extreme altitudes. Too cold up there for me....
You might think about the handling issues with a very large trailer. Things like filling stations, parking, backing into tight places etc. I am doing fine with my 25ft trailer, but anything bigger would definitely not fit into some places I have been at. Space (1 person, 1 dog) should not be an issue in any trailer with a separate bedroom area, and decent storage closets, like an old Tradewind, Safari 25 or Classic 25.
Good Luck to you!