Tony,
You have hit squarely on the value of self contained travel.
You need to get on line to RVParky and the other resources. There are lots of possibilities.
In a few states, the highway rest areas have signs posted as you mentioned. We have crashed in those a number of times and never been bothered. Most states do not have such rules. But then there is either Kentucky or Tennessee that plowed in most of the highway rest stops.
There are always alternatives to campgrounds. Learn to work the resources that are available on-line or by smartphone.
Matt