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My thoughts are you are ignoring the other great choice for your budget: the 100-400L. Optically as good (maybe better IMO) as the 300 f/4L IS, much more versatile, has better IQ @ 400mm than the 300 + 1.4, has better AF speed than the 300 + 1.4, although not as good as the 400 f/5.6L.
I've owned 300 f/4L IS, and 400 f/5.6L as sold both after getting the 100-400L, although I do miss the super fast AF of the 400 f/5.6L.
100-400L is not great choice for sports, but for everything else it delivers IMO.
Best alternative for everything is the Sigma 120-300 f/2.8 OS. It might be worth waiting for the new sport series version coming out, although you'll be up for around $3.5K, but it should address reliability issues and has distance limiters now for enhanced AF speed. Failing that carefully track down a current version of the 120-300 OS and prove to yourself it works as you'd like.