strange FM situation

[zaub3rfr4g]

i was trying a fewest moves solve and i found this strange situation which i can't solve in a nice way
i don't remember the scramble but i reconstructed it, so do
B' F2 R' D' R U' B' D L2 R2 U' L F L2 F' L F'
and try to find the best way to finish the f2l

 

[Stini]

My first decent attempt:
Insert an edge to F2L: R' L' U' L
2nd pair: U2 R D' B' R U' R' B
3rd pair: F' U' F
4th pair: U' R' U R

But I wasn't really satisfied with this since I didn't take an advantage of BL-edge, so then I went for a 2x2x3 instead:

Double x-cross: B2 U D L' D2 R2 (last cross piece was a bit lucky, I didn't plan it, but it's not always even useful to have the last cross piece solved anyway)
Last two pairs: U L U' B U' B' L'

That I'm satisfied with