Any field of human endeavor, there's more to it than meets the eye. You aren't the first to suffer this fate, and you won't be the last.
I, too, would find or make a "flushing wand," for this job as well as future "thorough cleaning" of your black tank. A flushing wand consists of a length of 1/2 inch PVC or CPVC water pipe long enough to reach down through the toilet clear to the bottom of the black tank, with a couple feet to spare. On one end put a cap and drill 3 or 4 holes to the side evenly spaced around the cap. On the other end, put a garden hose adapter. While you are at it, buy a valved hose/hose connector.
You can use that wand to fish around down there (yum-boy, what fun!) and break up the disgusting pyramid and flush it out the drain. Do remember to wear your safety goggles and rubber gloves while doing that job. Maybe a clear full-face shield would be even better.
Good luck, my friend.
