Unfortunately, I think you are correct in your assumption about the solution for your problem. Likely it comes down to a wad of toilet paper. We have a rule that NO toilet paper gets flushed. It goes into a small bag under the galley sink. Surprisingly, there is no smell from it.
You will need to disassemble and clear the joker valve and check all of the other valves in the pump assembly while you're at it. We replaced ours with a Lavac and been happy ever since. There are no small parts or flaps to fail, just a husky bilge pump.