Can't help with a TT but have done it staying in a tent with the DW before kids.
We were worried about reservations but couldn't plan with driving times. I did hear to reserve Yellowstone, so I did. Worried about making that reservation on time, we started on the northern route to get to Yellowstone first and planned to come back on a southern route. It was a little cold in Yellowstone in June. We even saw snow up high there.
If going with a north leg and south leg, plan accordingly. For a June-July trip, definitely start out south and come back north. If planning for late summer into fall, you may want to go north first.
That was 1998. We are taking the kids for our return trip this year. We have just about every night reserved. We aren't on as much of a shoestring budget as we were then. If we lose a deposit or two, oh well. I thought we'd try it this way.
The one thing I remember I didn't like about the trip was looking for campgrounds. Of course, that was before the days of widespread internet let alone mobile internet.
Good luck and have fun.
Oh, I also recommend not "stopping" until you clear the Rockys. Anything east of there could be visited on a shorter trip if you so wish.