Personally I would stay at a commercial/private park with full hook-ups.
Since this will be the end of a 6.5 week trip, I would utilize someone elses "dump" and thoroughly clean out my tanks, use someone elses electric to thoroughly charge my batteries, use someones elses facilities to "quick" clean the exterior of my coach and maybe slight maintenance.
You will be paying for your stay anywhere to camp so why not pay just a little more for your money. Also, IMHO you will have better luck getting reservations on such a busy national park.
GGeorge