I was thinking of using it with my 100-400 but after your comment affirmed what others have told me, that kills that.
What about with a 70-200 2.8?
A 2x on the 100-400 can be perfectly fine. In fact one of my pics doing that made it into the POTN coffebook.
Don't let people sway you off this decision that quickly.
Stacked 1.4x and 2x on the 100-400...