Use a toilet brush
We keep a toilet brush next to each head, wedged back behind the hoses so it stays next to the head. I expect my crew to use it when they engage the head for something serious. Why should either the skipper, or worse still the first mate have to clean toilets on the boat?
Neither my newly rebuilt Groco type K or my Ratitan PHII (with newly replaced pump) fills more than an inch or so. These are double acting pumps, they draw water in on one stroke, evacuate waste on the other stroke, and the dry/flush value just controls it raw water is allowed into the bowl.