Yes, your trip is very doable. Bryce will be the coolest. Just get up early and do your hikes and outdoor things and plan indoor things for the afternoon.
One thing I'd recommend is to cross off Yellowstone and save it for another trip along with Grand Teton, Glacier and that area.
Each national park has a great website with things to do, road information, special alerts, camping. Check them out. Here is Grand Canyon's:
https://www.nps.gov/grca/index.htmAlso, plan to stay in the parks themselves for the best overall national park experience and less time spent driving.
It's much better to see these parks with only a few days rather than not seeing them at all. You can always come back for more. Have a good one. Roll Tide! :)