We tag-teamed a "van supported" Adventure Cycling group a couple years ago on the TransAm. That meant the van carried their gear, but otherwise it was mostly camping. Their leaders were good about finding churches, fire stations, etc. across Kansas so the participants didn't have to sleep outside in the heat wave (we were a day ahead of them, and blew our budget on motels).

PacTour is another option, but I'm frankly intimidated by their long days.

I'd suggest you request a free copy of Adventure Cycling magazine. The back of the magazine has classified ads that include 4-6 companies running some sort of cross-U.S. tours. (Then join the AC organization, but that's another post!)