I have no idea for an actual alg, but this is how I would search for 1:
Most commutators are a 3-cycle of something, mostly corners, sometimes edges, but there is no reason why you couldn't make it a 3-cycle of 3 corner-edge-pairs.
If you look closely at the J-perm you see that it switches 2 corners and 2 edges. But with a U-turn you can make that 3 corners and 3 edges.
Now "all you have to do" is find some way to position the 3 corner-edge-pairs, figure out the actual commutator to cycle the pairs and finally undo the first moves.
I think I have actually done this for an FMC-solve at least 6 months ago (around the time I got my first 25 moves solution). The pairs were already in the correct position during the beginning of the OLL so I didn't have to use setupmoves. The commutator was 8 moves, but this is all I remember.
Why would you want this?