After I dump the tanks, I put a cap full of calgon liquid water softener and a scoop of the cheapest, powder laundry detergent I can find at the dollar store along with a gallon of two of water in the black tank. This rides with me home from the campground.
It gets sloshed around and coats everything and so far as prevented me from having any tank sensor issues. It also stays in the tank until my next trip where it is sloshed around again on the way to the campsite. Also seems to keep the tanks from smelling as I've never had any issues there, even with hot summer temps.
The grey tank has never been an issue but we wipe plates and pots off outside in the garage bag before going to the sink with them to minimize food particles in the tank.
If we have anything really grease covered such as bacon skillet or something along those lines, they get wiped with paper towels, washed in a tub of hot water out by the outdoor shower. Best use I've found for that shower handle as no one uses it for anything else except washing sandy/muddy feet off in my group. A big squirt of dawn dish soap down the sink followed by 3-4 gallons of hot water and then a ride to the dump station would be my solution if I had grey tank sensors sticking.