I have had 1D MK II, 1D MK III, 1D MK IV, 7D, 5D MK II, 5D MK III, and a host of other bodies. I personally think the FPS thing is overblown, I usually use single shot, but have also used 10fps and filled up my memory card with thousands of images, which I have to wade thru to find the one I would have likely taken using single shot.
AF accuracy goes to 5D MK II and center point over the 7D, but for focal length limited situations, I'd take my 7D, its good enough, at least as long as their is good light. It struggles as it gets to be twilight.
Maybe you should consider a rental. Rent a 1D Mark IV and you will have a excellent body that won't fail you when it counts. You can fill up that memory card in a few seconds, so take lots and lots of them aling... And make them biguns.