Do you have one of those sewer pipe 'caps' with the garden hose fitting molded in?
If so, with the black tank valve in the 'open' position, you could try installing the outer sewer cap, attach a garden hose (you'll need a female-to-female adapter) to a water faucet -
Turn on the water to pressurize the sewer pipes, watching closely so as not to overpower with high pressure - to see if you can 'blow' the blockage back into the black tank - usually this will do the trick quickly, as most blockages aren't lodged that tight, and not much actual 'pressure' is required...if things are flowing OK, you can use this system to backfill the black tank before dumping it again...
I've done this to also back fill the gray tank for flushing...
1. while doing the above - shut off the water faucet.
2. close black tank valve.
3. open gray tank valve.
4. turn on water again to back flush and fill gray tank.
5. turn off water.
6. close gray tank valve.
7. attach dump hose to sewer pipe.
8. open black tank to drain.
9. close black tank valve.
10. open gray tank valve to flush the system...
you get the idea...
Ray & Pat; Morada, CA