Even though it was Sony's intent that S-Log be used for later post color correction, we all know that often we find other ways to use tools. Just like FILM REC mode on the Panasonic Varicam was really only meant for film out finishes, but many people chose to shoot with in to get an extended gamma range and simply light and expose to that. Sony offers a very similar mode using their Hypergamma settings. The Japanese engineers might say that we're "using it wrong<" but so what if we like the way it looks?
Instead of the overly saturated, heavy-colored highlights look of Sony's Rec709, try this: shoot in S-Log and RECORD one of the Hypergamma viewing LUTs. I like the 800% with grey point at 40. You get an expanded Dynamic Range compared to Rec709, but with some protection from clipping at the top. Even more importantly you peel away Sony's color matrixing, which has the classic "Sony look" of over-saturated highlights that can both appear very Kodachrome-esque and can also lead to odd over-exposure highlight artifacts like white objects turning yellow. On film (and on the film-emulating look of the Alexa), colors desaturate as they reach overexposure into white. I much prefer that look.
Shoot in this mode and record it either externally or internally. You my find that you wish to add a little touch of saturaton to the final image, or perhaps not depending on your taste. But you won't have to go through a rigorous color correction and gamma adjustment, which is when the lower bit depth and heavier compression really bites you. Just light to this look and you can get stunning images out of the F3 which are remarkably better than the standard Rec709, no matter what you do in the Picture Profile menus. You can record this externally or to the SxS cards. It really turns the F3 into an altogether different camera.
Mitch,
I recorded with Samurai as per your suggestion and the whole video is green in color. What am I doing wrong?