Hi, last summer I went from Winter Park, CO up through WY via the Tetons, then north to Yellowstone, then departed from your proposed route. I started July 6th. Weather was great, a bit hot (but it was an unusually hot summer). Did Trail Ridge Road on day 2 of the tour, and yeah it was hard, but I you have to decide about altitude acclimatization based on your own experiences, that is so personal. I had some trouble, my tour partner did not.
Look on your map for Poudre Canyon just north of Rocky Mountain National Park - it's an additional crossing of the divide, takes you from Ft. COllins to Walden. The way we did it was a very long difficult day (50 mile climb, then 30 mile descent/flat with headwind) but it is unbelievably beautiful, and there are some places you could stop to break up the over long day. It's worth the pain. You end up in Walden.
There were some long distances in southern Wyoming between food/water sources, and you do need to ride HWY 80 for a bit near Rawlins, which sucks but isn't dangerous. It's hot and dry between Rawlins and Lander, with few services.
Oh and there is freakin' headwind every day - we were getting up before light to ride as much as we could before the 2 pm gales started.
We were camping, so can't answer your hotel question, but if you do it, make sure you stay at the cyclists hostel in Dubois (on the AC maps) it is stellar, and they had homemade ice cream!
No reason to go to Jackson if you don't want to, although it's pretty cute for a tourist trap. Jenny Lake is gorgeous, and there's a hiker/biker site.
The traffic in Yellowstone does suck, but it's do-able.
I don't know if we were on the transam, we were using AAA maps.
good luck, happy cycling!