The dreaded black triangle of whatever it is....

Yes it'll take time.
I took my garden hose with a high pressure tip, the kind that screws on with no controls,it ran through the window of the bathroom, the garden hose has about 55 to 60 psi pressure, I took the toilet cleaning thing and propped the valve open enough to allow the hose in about a foot (My pipe is straight down)then I turned on the hose for about 2 or 3 min. and dumped the tank, the idea being high pressure works good--just don't go away and have a beer!!!!