Troy, I think you could get good results with a 2x on your 600 f4 and a 7D2. I use the 2x on the 600 f4 IS II all the time. Mostly with a full frame camera. I also use it occasionally with a 7D2. In fact I did get my best photo of an Eagle in flight with the 7D2 at 1,200mm. Here's the image:
IMAGE LINK: https://flic.kr/p/q5VD8R
Rising to the Perch
by
SeattleBirdMan
, on Flickr
The v2 of the 600mm is probably a bit sharper than the v1 so I suspect it might help to stop down 1/3 or 2/3 when using the 2x. It is a very small focal length so it isn't easy to find a subject especially handheld.
I had a opportunity to see my first Brown booby in WA state a few weeks ago. Unfortunately the bird was about 1.5 miles away (according to google earth). It was flaying around for about 40 minutes so I had an opportunity to try both a full frame and the 7D2 on the subject both at 1,200mm. I ended up with more keepers and better focus in general on the full frame but 2 of the best from the 7D2 were actually pretty good. They come out with more pixels but I'm not sure if I'm getting more definition than the full frame. I made a collage of 6 images. The two upper left one are from the 7D2 and the other 4 are from the 1Dx. Each of the six images is cropped at 100% so you are actually seeing every pixel on the bird which is not a lot. At that distance there are so many variable I'm not sure if one could really draw any conclusions.
IMAGE LINK: https://flic.kr/p/zLt8yW
Brown Booby
by
SeattleBirdMan
, on Flickr
In conclusion If you have the money give it a shot. If you buy from a company like B&H or Adorama you can return it in 30 days fr a full refund if you don't think it is worth it.
Best
Doug