Your grey tank drains without a problem, doesn't it? You said that you came home with "... all tanks full ..." makes it sound like the grey tank isn't draining either.
I'm assuming that it is only your BLACK tank that has a problem. It's hard to know what's going on in your tank, but odds are it's one of two things: A tower of 'poo' and paper has built up below your toilet or a mass of 'poo' and paper is plugging the tank's outlet.
Sometimes, if you are lucky, sloshing liquids in the black tank as you drive down the road will breakup solid masses. You'll have to try dumping again to know if that happened. Sometimes pouring hot water down your toilet may break up masses of 'poo' and paper.
Trying to force water up, into your tanks with the hose connect on the sewer cap is usually not successful unless you have a very straight run. You also need to worry about contaminating whatever hose you connect to the sewer system.
You may need a 'wand' that connects to a water hose and then is inserted down through your toilet. Water pressure can then be used to breakup the clogs.
I'd suggest as a first step would be to get a clear sewer hose adapter that you connect between your sewer hose and your waste outlet connection. This allows you to see what is flowing through your sewer connection. Not pleasant, but it provides you with important about what is, or is not, flowing out of your tanks.
Sherm & Terry w/rescues Steve (std Poodle) & Eydie (min Schnauzer)
2015 Jay Flight 27RLS (Camped: 102 nights 2015, 90 nights 2016)
2006 Ford F350 6.0 PSD, Lariat, 4WD, CC, LB, SRW, auto., Camper pkg.