I did a similar trip from Charlotte to Los Angeles back in March of this year. I went down to I-10 for the trip West, and came back I-40.
East of the Mississippi, superchargers are so frequent along the interstates that you should be able to skip some. Once you get out West, you may want to stop at every one, just to be safe, or because as an excuse to stretch your legs anyway.
I had reasonable success with hotel chargers, either Tesla or J-1772. I was able to book a reasonable hotel about half the nights of my trip, and a couple of times that I couldn't it was because I waited too late and the whole hotel was sold out. (The road trip itself was half the reason I was taking it, and I was really winging the route.) At least once, if I hadn't called ahead and asked them to put a traffic cone in one of the charging spots, it would have been ICE'ed, so I recommend you call ahead to every hotel that you hope to charge at.
Sounds like a great route, despite the summer heat. Good luck; I hope you have fun!