No way to tell about the travel situation. However Zion is very hot in summer, often well over 100 deg., as is Arches. Both are overrun with tourists, Arches so bad that they have frequently closed the gates. Zion will have a line stretching out for miles outside the gate, and I hear they are also thinking about closing the gates on occasion. Bryce is higher and cooler and less popular, Capital Reef is less crowded but also hot. The mob scene is reportedly because of the ad campaign that Utah Tourism ran in big eastern cities and Europe.
All of these crowd predictions are based on normal years, this year will be an outlier.
Glacier isn't so crowded, Yellowstone is crowded. There are Lassen, Rainer, Crater Lake, North Rim of Grand Canyon and Olympic which are cooler. With three weeks you better pick one or two parks to concentrate on.
As for Alaska couldn't you fly up and rent an RV?
