I'm also in a position of trying to find a good birding lens to go with a Canon 80D (which I've decided is the camera I'm upgrading to this month). I have a friend from college who does professional photography with his wife, and here's his suggestion:
This one is going to be your holy grail, so to speak. The price is pretty much up there, but it's something to aspire to. It's prime audiences are wildlife and sports photographers (for obvious reasons):
https://www.the-digital-picture.com/Reviews/Sigma-150-600mm-f-5-6.3-DG-OS-HSM-Sports-Lens.aspx
I had already been looking at the Contemporary rather than Sport. I'm still trying to decide how critical of a factor the extra weight that comes with the Sport is, compared to the superior construction and specs the Sport has over the Contemporary.