Here is how to solve the "parity" configurations using a slightly modified Waterwheel Sequence where the left and right twists are to the inner slices instead of the outer layers. As can be seen below, the initial starting positions are different. On the second cube there is an initial setup move of a half-twist to the back face. The waterwheel sequence is the first nine moves (2-10 on second cube) which creates another pair of swapped edge cubies, the result can then be solved using the aforementioned 6-color sequences.