I know people are quick to discount the 70-300L because of the variable aperture, and the dreaded f/5.6 on the long end, but it's not actually THAT slow. A reason to discount it is if you do need the 400mm (you seem pretty eager to get to 400mm somehow), or you can afford the f/2.8 lenses. Compared to the 70-200mm lenses f/4, I'd rather take the 70-300L, but everyone's reasons and needs are different.

I'm not pulling up the review to get the exact numbers, but it breaks down something like:
f/4.0 - 70-112 - Same speed as the 70-200.
f/4.5 - 113-154 - Slightly slower than the 70-200, fairly insignificant.
f/5.0 - 155-224 - 2/3s of a stop slower, which is significant, but only over 45mm of range. The 200-225 range is infinitely faster.
f/5.6 - 225-300 - The dreaded f/5.6, a full stop slower!, but on a focal range the 70-200 doesn't even have, so this is actually a plus.

Apparently Sigma 1.4x extenders do work with the 70-300L, but I have not tried it.

It's cheap, sharp, has a newer 4-stop IS, has some weather resistance. It does extend as you zoom, if that puts you off.