Here are my options to decide from
1. Buy 70-300mmL and sell the Non L (may be buy a kenko teleconverter in the future)
2. Buy 100-400mm and keep 70-300 Non L for travel
3. Buy 100-400 and sell the 70-300mm Non L
Some parallels between you and me. I upgraded from a 40D to a 5D3 last fall. I have a 100-400L and was contemplating a 70-200 2.8 ISII, but decided (mostly due to an upcoming trip where I will be highly mobile and after dragging the 100-400 around Tokyo) to get the 70-300L instead.
I have to say I am really pleased with it, and find I do not use the 100-400 very often any more. Zero complaints on its performance, and the shorter reach, while every now and then a drawback, is often mitigated for me as the resolution of the 5D3 lets me crop to get the composition I wanted anyway.
To really know which I'd lean towards in your shoes though, I'd need to know how important weight, size and portability are to you. It looks like you are doing a lot of hiking and outdoor work (somewhat similarly to me), so I
think you would end up appreciating the 70-300L. On the other hand, for the bird shots, you will end up using the longer range of the 100-400 more than I do I think.