Such a simple question, I'm not sure why it wasn't answered already.
I'm not a sports shooter, so consider this an outside opinion. I would keep the 70-200 and get the 300 to go with it for its bright aperture and amazing focus speed. One 1.4x TC could be shared by both, but I really think you need some sort of a second body so both are ready to fire when the right shot comes.
I have a friend who shoots high school sports and he makes good money with this combo.
I would consider the 200 f/2. You could put a 2x converter on it and make it a 400 f/4. Or take it off and have a really nice 200 f/2. I think that's the most viable option to switch things up all the time. If I had the money, I would buy one right now. Maybe next year!
Consider renting a lens or two before buying one. You will quickly learn whether it is a good choice for you. For sports you do not need VR so an older used non-VR telephoto would make a good buy.
Appreciate the weight difference between your 70-200mm as compared to a 400mm f2.8 or 500mm f4 for extended use and moving around. Pro shooters with a monopod are usually not allowed to move much so it is not a concern.
For general wildlife shooting most photographers favor the 500mm f4 as it provides excellent reach but can be used without a tripod. For sports a lens to consider is the 200-400mm f4 lens and VR I or VR II is not really going to make a difference in your pictures.
Although if you are shooting sports and rely on AF, your going to want AFS.
Really this just depends on your budget. You already have a very nice setup, so if you do get another lens I would just go for the longest prime you can afford (400 2.8 certainly will not dissapoint!)
I have personally used the 300 2.8 AF-D though and the image quality is OUTSTANDING
