We visited Yellowstone in August 2012, our best times were near dawn and dusk.
Waking early is not for everyone. Most folks wont do it, which is why it's a great time to travel the Park. You see more in less time without the 5 mile back-up. Dinner time to dark was also not as crowded as midday.
We saw more animal activity between 6:00 and 8:00am than we saw the rest of the day. We went to view points with no parking issues, had trails to ourselves for a little while. We'd bring a thermos of coffee, and a portable breakfast to enjoy. Good times.
You may find July busier early in the morning but suspect it will be better than later in the day. Its worth a try if the crowds get to you.
Most days we left just prior to sunrise to see wildlife and watch sunrise, took a mid day break/nap when the Park was super crowded. Worked well for us.
Enjoy!