I have been planning to get a 100-400L IS to complement my 70-200L IS and 1.4x tc. While I was also considering the 300mm f/4 IS, and can get to 420mm with the 1.4x tc, I generally prefer the convenience of the zoom. However, if I get the 300 f/4 and a 2x tc, then I can get to 600mm with that combo, and if the results would be much better than the 100-400L with the 1.4x tc, then it is something I will seriously consider doing.
I know the 300mm plus the 1.4x tc is a great combo, but how much worse is the 300 plus 2x tc? I did a search and didn't find anything relevant.
I've used my 300 with a 2x shortly, but that wasn't much good, not very sharp at all and contrast down the drain. And no AF ofcourse.
If you really want to reach that far I'd go with a 400/5.6 + 1.4 TC.