Another vote for keeping it to 300 miles per day max.
One thing I don't think has been mentioned - you will be stopping more often for gas, the number of gas stations where you can safely fuel,up will be less and the process will be more involved pulling that trailer. Don't wait until your tank is almost dry!
Watch your overhead clearance and don't get yourself stuck at a pump where it is impossible to exit.
Also IMHO if I had the time you do I'd opt for one of those parks and leave myself more time to explore it. I guess my choice would be Yellowstone and it's environs. The south entrance to Yellowstone leads directly to Jackson Hole and Grand Teton NP.
Enjoy the trip no matter how you decide to do it.