Usually while the grey water tank is discharging, I go inside and treat our toilet.
If we are going to another campground, this process usually involves a couple of steps.
First, I simply run a couple of gallons of water into the tank. I then pour a little water softener into the tank. Once we begin traveling down the road, the numerous starts and stops will cause water within the tank to slosh around. This, in turn, will cause the water softener to splash the sides of the tank, thereby coating them so that future discharge may not stick to the sides.
Another trick I may use when heading to another campground is to pour some ice into the toilet, allowing the cubes to go directly into the black water tank. I always try to do this the very last thing, for I want to get the rig in motion before the ice has time to melt. The ice, like the water softener, will slosh around. Since the ice is in a solid state, it will actually dislodge anything that may be sticking to the sides of the tank.
Both of these tricks, combined with the black water flush I utilize, help to keep the black water tank clean.
Once we arrive at a new campground, I will usually open the black water tank to discharge the water softener. After closing the tank, I then return inside, add a couple of gallons of water to the tank, and then add our toilet treatment.