'Real world' drive times.
You certainly do not want to do your drive times based around the unrealistic predictions of a computer program that does not need to stop to eat, use the bathroom, sleep, nor does it consider other real world details like possible construction and congestion delays, or weather for that matter. Eight hours on the road will average between 450 and 475 miles without any major sight seeing, just the basic stops. You could reach the Grand canyon south rim on day 1, or at least to the nearby towns of Williams or Tusayan. It would be possible to reach Moab next day, but wouldn't leave much time for sight seeing at the GC and Monument valley and that's where you need to work out your priorities. Keeping to 8 hours a day you will need around 6 days to drive home from LA so if you don't set out until the 24th you are already looking at the 30th before getting home with a day spare perhaps.
If you decided on I70 then Grand Canyon, Moab, Denver, Salina, St Louis and Columbus would make reasonable stops as in distance, giving you a slightly longer last day, or break it up into the following morning. Personally I would aim to take a slightly slower pace in the west at the start and then have a couple of longer days at the end of your trip, where you might be more familiar with the area, or are easier to visit from home during future trips.