So in the pictured situation, I would normally do a JPerm:

and I always do the jperm on the right, so I have to start iwth a U2, like this:
U2 R U R' F' R U R' U' R' F R2 U' R'
This approach is 14 moves. I have not worked on my fingertricks/speed, so this takes me around 6 seconds (I realize this probably sounds ridiculously slow, but that's actually a pretty fast turn speed for me as I try to look ahead to LSE).
My analyzer suggests that I consider this alternative:
R2 F2 R U R' F2 r F' R
and honestly I can't see what's wrong with it. It's 9 moves, which is a _lot_ fewer than 14. The three F moves are bound to be worse than R/U for some people, but I would expect I could execute them reasonably.
I'd appreciate people's comments on these two approaches to this case.
Also, if I have asked this in the wrong forum please let me know.
Osric