I agree with Rick - the best 'compromise' (in the sense of uses, not quality) is the 1D X. The one downside is the 'loss' of the 1.3x crop of the 1DIV - but, some recent comparisions posted by Richard Lane of the 1DIV+500L II vs. 1D X+500L II+1.4xIII (a couple of pages of them!) show that you have to look really hard to see a difference in IQ there, and even when there is a difference, it can go either way.
Also, since you mention both the 500 II and the 600 II, I am fairly certain that the 1D X + 600 II would beat the 1DIV + 500 II. Not sure if you've used the 500 MkI, but the new 600 II weighs about the same as the original 500/4 IS, and I can tell you that for me, at least, the 1D X + 600 II combo can be handheld (I do have a nice RRS tripod and gimbal, but the shots below are handheld, click for larger).
I think for the uses you indicate, assuming you can afford a long enough lens for birds/wildlife on FF, the 1D X is the way to go. In particular, the high ISO performance is stellar. I notice you have the 7D and 5DII, and I did as well. Everyone's tolerance for image noise is different, but personally, I preferred to keep my 5DII at ISO 3200 or lower (6400 for 'emergencies'), and my 7D at ISO 1600 or lower (although before the v2 firmware I ended up at 3200 a lot with Auto ISO). With the 1D X, I find that ISO 12800 works as my normal upper limit, with ISO 25600 for 'emergencies'. Both shots above are ISO 6400, and this one is ISO 12800:
Good luck with your decision!
--John