We wouldn't travel over 300 miles/day on that long of a trip if you're retired and have the time. Working vacationers do more. Pull in early afternoon, relax, have a nice meal, maybe some siteseeing.
You have 2000 miles which at 300 mi/day would be 6-7 days of travel. If planning to sitesee or spend more than an overnight at stops then add days.
No need to make reservations enroute if you pull in early and stay away from major attractions. If worried then call early in the day or day before so you can better judge where you'll end up. If you're going after summer better yet. The Canyon is great in Sept/Oct.
For Grand Canyon... have reservations.