Your dilemma is the same one I went through last year: loved the f4 IS but found it a bit short for the sport I photograph.
I tried it with a 1.4 extender (as others have said, you lose AF with the 2x), and while it worked fairly well, the extender did slow down the AF somewhat. I came to the conclusion that I was going to need a different lens. One of the things I really liked about the f4 IS was its size and weight, so the 100-400 was a bit of a stretch for me; I'd already sold a 70-200 f2.8 because I hated carrying it around. So I rented the much smaller 70-300L ... and was blown away by the quality. The extra 100 mm was enough for my needs, and the lens was only slightly heavier than the f4 IS.
I dithered for several months, but in the end I got a once-in-a-lifetime deal on a used 70-300L, so I bit the bullet and sold my f4 IS. It was a wrench to see it go, but I haven't regretted getting the 70-300L; it's an outstanding lens, lightning-fast AF, terrific image quality.
Bottom line: if your f4 IS is often too short, you're probably going to be better off with a different lens. An extender is fine for occasional use, but not, IMHO, as a regular solution.