IMHO your going to have to use a stick, coat hanger, or small snake to dislodge this blockage. If your concerned about a snake, or the stick/hanger getting stuck due to it's end configuration, take black tape and wrap it around the business end and you'll have a smooth "battering ram" to break through the blockage. Others may say it wouldn't work--believe me it does. I've used it on mine and several friends that were experiencing exactly what your facing.
I don't see where the black water flush is going to help you much as your stoppage has got to be in the down tube and the black flush can't spray at an angle to reach up into that tube.
As a last resort, and I think it should be the last resort. put a high pressure nozzle on your flushing hose, open the toilet valve (with water off) and stick the nozzle a few inches into the toilet down tube and stuff a towel/rag around the hose to keep the water from backing up. Have someone turn on the water to the hose and keep pressure on the hose/rag and see if the high pressure will blast it out. Nothing you do here can physically harm the RV, the thing you don't want to happen is for the water to "blow back" and splash brown water every where or the blockage to not let go and your toilet start to fill up with brown water. To minimize these risks, have VERY good communication with the person outside turning the hose faucet on/off!!
Days camping (2015)----88 days
Days camping (2016) ---110 days
2016 Wildcat MAXX 28RKX (33' TT), 2007 13' Scamp
2015 Ram Laramie Hemi
30 years RV'ing
12 different RV's