I use a 70-200 f2.8 IS II. Not the f4 model
Ah! Sorry! At least you do have the f/2.8 II, though...that's a great lens!
So if I drop one stop of aperture, I bump up one notch of ISO? I'm looking through my library and trying to gauge the ISO's, apertures and focal lengths used and what I could wish for.
You either notch ISO up a stop, or, if you have shutter speed to spare, you reduce shutter speed by a stop. I don't shoot motorsports...I do shoot my friends model airplanes in flight every so often. Owning the 7D myself, with it's smaller pixels, it's tougher to get away with reducing shutter speed unless you specifically want some motion blur. So generally speaking, every stop of aperture lost usually means a stop increase in average ISO used.
Of the events I've been to, most of the time 200 is more than enough, but as a spectator there is only so close you can get to the track, and catch fencing does rather limit your view a lot of the time.
Airshows, again 200 is more than enough a lot of the time, however there are times when a bit more reach for the smaller planes (biplanes, spitfires etc), or when they are manoeuvring further away would be useful.
Wildlife is third on my list after motorsport and airshows.
Since wildlife is the tertiary activity, then I have another option for you. I don't know what your budget is, although it sounds like $2500 may be around the limit? I have been subscribed to CanonPriceWatch.com for a few years now. I have a number of alerts set up in their system. Over the last couple of months, I've been getting a LOT of alerts about Canon's Mark II telephoto lenses. Several times over the last week and a half, I've been alerted of USED Canon EF 300mm f/2.8 L II lenses clocking in at ~$2700-2800. Given the list price for that lens, that is a superbly good deal!
For your motorsports and airshows, I really don't think you could do better than a 300mm f/2.8 II. It's eminently hand-holdable, the big aperture is ideal for the kind of fast moving subjects you shoot, and it easily adapts to 420mm f/4 with the 1.4x TC, which is still well within the realm of usability. If you really need it, you can always slap on the 2x TC for 600mm f/5.6 performance. I rented this lens a couple times a year and two years ago. I used it with both teleconverters. IQ with both was EXCELLENT. Even with the 2x TC, it performed as well or better than my 100-400mm lens, and the boke was always superior, regardless.
For $2700, even though that might be a bit beyond your desired budget, I really don't think there is a better lens for the kind of subjects you photograph. These deals come an go, and I've seen the lens sell used for as low as $2399. I'd go to CanonPriceWatch, find that lens, and set up some alerts for the used price range you would find acceptable (I'd say $2300-$2900 is very good for used), and take advantage of the next deal. New, this lens costs about $7300, and new deals rarely go below about $5500. I myself will probably be picking up a used copy, so long as it was well cared for, next time a $2700 deal rolls around. It's just too cheap to pass up.