Here's a few tips that might help:
1) As others have said, start by putting in several gallons of water before you leave the house on your trip.
2) Put in a cupful of Calgon water softener to slosh around in that water as you drive. The Calgon makes the inside of the tank slick, and keeps solids from adhering.
3) Use LOTS of water per flush, and keep the dump valve closed.
4) When the tank is almost full, pull your dump valve. The large amount of water, coupled with the WEIGHT of that water, will push the solids out very quickly.
5) Put several gallons of fresh water back into the now-empty tank, along with another cup of Calgon.
6) Just before you leave for home, put a 5 or 10 pound bag of ice into the tank via the toilet bowl, with a bit more water. As you drive home, the ice will slosh around and scrub the tank interior clean. When you get home and dump your tanks, you'll be surprised at how much debris was still in there after you dumped before leaving the park. Get a 6" clear plastic extension to add to your sewer connection so that you can actually SEE what is flowing.
I do this every trip and have not had an issue now for YEARS. It works for me.