First, your cameras are okay. I've used EOS-3, Elan 7, A2E, 1V, 10D, 30D, 50D, 5D and 5DII on my 500mm and they all worked just fine. You might want to consider a 50D, 60D or 7D to replace the T2i... mainly for the AI Servo tracking. Yeah, a 1D would be great, but it's bigger and a whole lot more money, and personally I prefer 1.6X crop over 1.3X.
Second, 500/4 IS is the lightest and most compact of the three you list, and it ain't small... I've handheld it briefly, but use it with a Gitzo 1325 tripod, Kirk BH-1 ballhead and Wimberley Sidekick most of the time... Both the current 600/4 IS and 400/2.8 IS are not recommended to use on the Sidekick, due to their weight (I know some people do... Wimberley is just covering their arse by not recommending it.) Basically, $1000 to $1500 budget for a tripod, head & accessories, too, if you don't already have a solid one. At least, you'll want a very substantial monopod.
Next, you mention some of your uses... I shoot sports, wildlife. Sometimes with 5DII, but mostly 7D and before that 50D... for the "free" 1.6X teleconverter and the tracking ability. 5DII is fine for some wildlife, but really not ideal for most sports or fast moving subjects. It's AI Servo tracking just isn't up to it.
My 500mm sees fairly limited use for sports. It's too long a lot of the time, but I have close access to most events. I did use it from the stands at an equestrian event in May.... looking for high angle shots that eliminated busy background.
I use two 300mm (f4 handheld, f2.8 on tripod) far more often, sometimes with 1.4X teleconverter.
I do use the 500mm some of the time for particularly long reach sports shooting... Cross country equestrian events, cycling, motorsports.
Yes, the 500/4 and 300/2.8 both take 1.4X and 2X (both of mine are II) quite well.
I can't see taking 400/2.8, 500/4 or 600/4 to a zoo, either. In fact, zoos in my area wouldn't let me in with it. I'd take my 300/4 instead... it's hand holdable and reasonable to carry around all day, and I might be able to sneak it in past the gate.
My 500mm sees a lot of use with small wildlife... birds, small furry critters. In the field, though... not so much in zoos.
With any really long lens, you are to some degree at the mercy of the environment. You are shooting through a lot of atmosphere so any dust, haze, fog will heavily effect the quality of your shots. When you don't have good conditions, you either incorporate it in your shots, or switch to a shorter lens and concentrate on nearer subjects.