As you seem to be a peripatetic wildlife/bird photographer , meaning lottsa hiking and hand-holding of your photo rig, and assuming you are of average physical strength and endurance, then I think your mobility kit should include 400 f/5.6, or 100-400 or 300 f/4+1.4TC or something else 3rd party in the same weight bracket.
However, if you are a sturdy type or willing to suffer a bit and hopefully beef up, then the 300 f/2.8 +1 Series camera becomes tractable for extended periods of time (i.e., 2-3 hours).
I have gone thru a similar process with the 300 f/2.8L (non-IS) and the 200 f/1.8 both of which are about 300g heavier than the 300 f/2.8L IS. A heavier rig than that I have not tried hand-holding , nor would I really want/need to.
When it comes to IQ, I think the 300 f/2.8L +1.4xTC is practically as good as the naked lens. However, I have not used the 2xTC on the lens much because of the AF becoming sluggish.....and to me the AF speed (and IQ) is at least as important as the focal length (reach).