Agree with some of the great suggestions you got so far. We've done 3 trips across the US of 32 days or more and a lot of what you've been told is standard operating procedure for us.
Tires - yes, check them on TT and TV and don't forget the spares. I always take a pressure gauge and bought one of those laser/infra-red thermometers to check tire & hub temperatures when we stop.
Bearings - could be worth the peace of mind to have your trusted RV service shop repack them. You have a pretty ambitious schedule and a bearing failure would ruin a LOT of your plans.
Clearances - know them.
Weight - before we leave on any extended voyage all the unnecessary stuff comes out - television, extra chairs, even dishes and utensils. I get that trailer as light as possible. Weigh your rig loaded and ready for the road if possible.
I also agree with others in that you should plan to balance those days of hard driving with a day or two off the road. Add some days to your itinerary if you can, and yes, be open to unexpected attractions that are not in your original plan.
Yellowstone - specifically, make sure you stock up on food and other consumables before going in to the park. If you have to restock in YNP you'll find it very expensive and not a lot of things to choose from. Gas - nothing you can do about that as you'll likely be doing so much driving in the park that you'll have to bite the bullet. Be sure your furnace is in good working order, you have plenty of LP gas, and warm clothing. Nights at Yellowstone can be very cold, even in July. Case in point - we left YNP on the morning of July 5, 2004. It was 37 degrees.
Enjoy & safe travels.
