If you're at all worried about perfection (your choice of 1D X and 24-70 II indicate you are), you will not be happy with the performance of the original 70-200/2.8 IS at anything brighter than f4. So why have the mk I when the f4 IS version can do everything that lens can do well while being cheaper, smaller, lighter, and optically better? Also, when shooting Tv the lens can't open up to apertures with sub par performance.
Having said that, the 70-200 II really is something else, and that is the one you'll be thinking of should you settle for anything less. You chose f2.8 for the normal zoom to stop action, so why not get the same for you tele zoom?