For motorsports (road courses with a lot of opportunities to walk around) I use a 70-300L and 400 5.6L. Used to use my 70-200 2.8 mkII, but I found I was fiddling around with teleconverters too much. Also used to use a Sigma 120-300 2.8 OS, but it's a big lens to lug around in the heat all day, and I don't like using a monopod if I can avoid it.
So- I've tried some of the combo's you're considering, and found that when I combined weight/IQ/cost/convenience standpoints, the 70-300L and 400 5.6L gave me the best options, with only one lens to switch around if needed, in a lightweight package. I also find the lens hoods easy with this combo- the 70-300L is small enough that I just put the hood in position and leave it there for the day, and the 400 5.6L has a hood that pops out itself.
Also note- I've used a non-reporting Kenko 1.4TC with my 7D on the 400 5.6L and had good results with focus on everything but the center focus point. With a 1D MKIII the 1.4TC would be great on the 400 since it's actually designed to focus at f/8.