I think the reason you are seeing stuff still come out after more than one dump is because "stuff" gets into the corners when you just sit in one spot and are not moving around thus mixing the contents. The tank rinser does not reach them well enough - especially the corners on the same side of the tank as the rinse nozzle.
I found that while snowbirding in Florida for 18 years and staying in one spot for 3-4 months, I had to use the wand down the toilet hole about once a month to blast the stuff out after normally using the tank rinser every dump. It would take quite a while before the water ran clear too because the stuff packs quite tightly into the corners!
Here is the one that I use. It does a good job and shoots a powerful blast of water. I would use it down the toilet while emptying with the macerator.
Barney