I have the same HF 18 lb. unit that you described. I have really only used it a few times, so my experience is very limited. I can not really answer your questions, but I'll be interested in seeing any replies that you get.
When I used it, the unit was sitting on a concrete floor, and it did not move at all over the course of almost two days. I was doing an experiment to see how well I could deburr several 4" x 5" x .5" aluminum plates into each of which I had drilled a dozen holes. I filled the bowl with the green pyramid media, and used water with a cap-full of Dawn liquid dish detergent. It was probably at or close to the 18 lb capacity. I did not try circulating the water/soap mixture through a filter, but it would probably have been a good idea (because, as you have noticed, the water becomes very dirty after a while).
As for results of my test, I believe that my parts were too big for the bowl. I got inconsistent surface treatment from one plate to another (probably due to some of the plates sticking to or rubbing against each other). Small burrs were removed, but a few larger ones were not, and I probably should have attacked those with a quick turn of a countersink before putting the plates into the bowl.
I'm not sure that I understand the goal of using the bowl-within-bowl approach...