Most of the parks I stay at (one exception) have only one or two dump stations that are "All source" dump stations, unless that is they have full hook up sites. (The rest of the parks I stay at have full hook up save that one) The one has gray water dump sites, as does one other park I have visited once.
When I am in these parks I tend to choose a site that is close enough to a gray water dump that I can simply pump gray into it if I have to, which I do not often have to do (long story, but I can easily go over a week by myself, with a wife I need to dump more often but alas... No more wife).
I will get a tote when next I find a traveling companion, (A good 40 gallon one will cost .. A LOT).
And I will dump first black, then make a 2nd trip for the gray.
Oh, I'll also have to design a tote hitch for my car (this will be a 300 pound rated hitch)