If you have a pull down rod for your shade , use it for a clean out snake. Turn off your water outside so you can use your on board water and open the float valve. Poke the rod down and wiggle it around. Works great and you can get the clog out. Then as suggested, lots of water with each flush will keep problems away. If you are going to use the method of putting water in and driving around sloshing water to break things up, put ice cubes in the tank to help the process. Not just ice but cubes to do the best job.
Happy travels, Arnold