I have gone down this path and ended up with the 300mm f/2.8 IS II, but I'll admit that even with the 2x III, I sometimes wish it were longer. I also took the 800mm for a spin (as a CPS loaner) and frequently found it to be too short, even with extenders. Yes, you read that right. With my shooting (everyone is different), I find my subjects are either in the 70-200 range (often with 1.4x) or in the 300-600mm range. Beyond 600mm, I really need a 2000mm or something as they are way too far away. Plus, here in Florida, the heat mirages and humidity really much up shots beyond about 50 yards in good times and beyond 50 feet in the middle of summer. With the extenders, you have an amazing 300mm, excellent 420mm, and very good 600mm (esp @ f/8).
The other key for me was portability. The 300 2.8 is a lens you can carry with you and hand-hold, while the 600mm is one you lug with you really need a tripod (and gimbal) for in most situations. I often hike in or stalk my subjects and this is really important to me. If I was shooting out of blinds, from a vehicle, or stationary position most of the time, the 600mm would be my choice, no question. It's definitely a lot more effort to get close to your subjects, but one of the things I love about wildlife photography is the very challenge of getting the shot.
Also, the 300mm leaves me with enough spare cash to buy a 1Dx one of these days.
Of course, there's always the 200-400 1.4x, that gives you more options, but is still large and heavy.