The point of doing the parity algorithm is not to solve the cube immediately. As you have said, there is no algorithm that will directly solve this case. However, after doing the PLL parity algorithm, the cube will be solvable. It won't be solved, but you will be able to solve it with the algorithms you know. That's the point of doing the algorithm. When we do a 4x4 solve, if we get to PLL and we see that the cube has parity, we don't do a single algorithm; we do the parity algorithm first, then continue normally. You should do the same thing. It will set you back a bit, but it's necessary if you want to go forward.