If the valve is open and the liquid is up in the toilet then you will need to snake it with the valve open, keeping plenty of water in the tank to flush the tank once you get a path through the poo. Perhaps one of these or something similar will help.
Valterra: RV Hydroflush Archives - Valterra.com | Valterra.com
SKU: F02-4100, RV Hydroflush 45°, RV Hydroflush 90°, SKU: F02-4110
This would allow you to keep your black tank hose connected, then uncap and drill out or what ever it takes to open up the clean-out port and run a plumbers snake through it and into the black tank. An electricians conduit fish tape may work also. Or you may be able to snake from the top, through the toilet. In which case you would cap the clean-out port mentioned above. It will not be pleasant. And I'm sure most RV techs will be too busy for the job, even if they have nothing to do. I assume you have "T" paper in there too, which adds to the issue.