Pick up one of these......hook up hose and back flush after dumping black tank..then with water still running close black tank valve.
OR install a back flush kit on your black tank.
The reason you want to add a few gallons back into tank after dumping is so bottom of tank stays wet and the few gallons will slosh around as you drive.........sloshing/wet helps keep any stuff from sticking and drying out.
OR just have some one stand by.......open slide out/flush toilet bowl of water down into tank while you are dumping grey tank