You will find many RV parks along major highways. And most private RV parks will have sites long enough for you. National, state, and COE parks may not. And height will not be a problem along primary highways.
400 miles is a long day. 500 miles is a very long day. With stops and driving on a major highway you can plan on averaging around 50-55 miles per hour, no matter how fast you drive on the road.
Generally you will not need reservations at private RV parks along the way unless you happen to end the day in a popular "destination" area. If you want to stay in a national or state park with hookups then reservations are usually necessary. There are web sites such as rvparkreviws.com and smart phone apps to help find RV parks along the way. I try to plan ahead on about where I will be at the end of the day and at least call ahead about vacancy or go ahead and make a reservation. Last thing I want to do after a long day's drive is to pull in an RV park unannounced and find it already full. I don't do parking lots. We frequently stay at KOAs. They are sort of like Holiday Inns, fairly consistent, generally nothing special but generally fine for a place to stay.