I'm not quite sure what you mean but I feel like the standered is R U R' F' R U R' U' R' F R2 U' R' U' I know the centers don't move at all with that one.
I interpreted it as affecting the centre, period. Meaning, no switching, no twisting. As in yours, if you add a U' at the end (so it's parity), it twists the centre in place. That being said, I don't know if he's looking for a J-perm from parity.
I'm not 100% sure if I'm right, but a J-perm is parity because you're swapping 2 edges and 2 corners, and cannot be solved with a commutator (unless you add in AUF; closest I can get is F2[r2, D' L2 D]), and you have to twist a centre in place in order to solve it, as far as I know.
Why do you need one anyway? Trying to solve a supercube?