as an extension of my knowledge of F2L I would encourage you to turn it so that the Green face is your Front face. In that case you could use this algorithm. U' L' U' L U F U F'
If you pay attention to it enough you can develop an intuitive sense of how this works. It is a very simple idea of matching the corner to the edge to create a corner edge pair.
If you really dissect it you can see that U' L' U' L sets up the corner and edge pair such that it can be easily inserted. The corner piece you are manipulating is on the upper layer, and directly above where it will end up. A white sticker faces you, green up, and red left. If you notice there is the edge you are trying to pair it with on the upper layer, on the right. It has red facing up. As you do the next move that both joins these pieces together and inserts them into their correct position, you will see how the first F move joins the pairs, the U move rotates them into their correct slot which was just rotated to the Up layer, then the F' move simply restores the cube, except with a correct corner edge pair. This joining of the corner edge pair, and eventual insertion is the cornerstone of intuitive F2L.
EDIT: Fix something, also I like the first alg you presented there, but it is a little lacking on the intuitive front... So I didn't not use any part of it.
Ramble off....