While you are towing with the TC/TT combo, you are only towing it to and from the west. With the TC, you have the ability to quickly leave to go 100 or 200 miles away for the weekend without towing anything. You wouldn't want to go sightseeing in the car for 200 miles and then have to come back to sleep. Plus, the TC would always be ready to travel while with the Class C, you would have to store a lot more stuff which I see would become enough of a hassle to prevent you from traveling some weekends.
You could also go with just the TC for a while to determine if it isn't big enough for you. Do just the TC for the first year and then hopefully convince the boss you can travel while you do your job. My wife and I have no problems going out for 4 weeks in my small 8' TC. There are also a number of folks who live full time in a TC.
Not saying this is the best option as that is a personal preference, just trying to give you some additional ways to think about it.
Good luck and remember those of us stuck to a desk in one location.