I try to limit myself to 4-6 hours a day. If there are two drivers, I am sure you can extend that. My Oregon trips usually take 3-4 days when towing, and I try not to do any one day marathon style.
After you stop, remember you are going to have at least a small set up to be comfortable and rested for the next day. I don't like to make a fuss after sitting that long so think of what you can do to minimize the daily set up and strike the next day.
When I do a rush trip, I try to keep as much in the car as possible so I can just open the trailer door and have space. Traveling with dogs (and now a cat) makes that hard tho.
In June in California, you will have heat to deal with, but once you get out of the central area, you shouldn't need to worry about being comfortable.
One mistake I am going to quit making is trying to be cheap on my stops. RV parks are far easier as far as set up than camping parks, (No water hauling, dumping, setting up
solar panels etc) and as mentioned above.. I am tired and want a little luxury like TV and
air conditioning. This year, on my way to Oregon, I am going to do I-5 straight up and skip the scenery and quaint parks. In the long run, I may have spent a few more bucks on parks, but it will be an easier drive and more restful at nite. They are also a LOT easier to find than camping parks. Especially in the central valley.