Heya,
It's all about compromise.
There's a lot to consider, and it really needs to tailor to your needs and your situation of actual shooting. Ie, what size birds and distance, and in what light, perched or in flight. Ie, what size animals and distance, and in what light. I think it may be safe to say that stressing in flight and chasing things around is not the goal, but that's for you to decide. This is why it's important to consider what you are actually doing for your shots, and not just what we all think.
I look at it like this though, for a casual shooter that will just shoot what they happen upon at any given time, with no preparation, a zoom is simply going to be the handier tool. It let's you quickly react and potentially capture something at various ranges based on where you physically are in relation to the subject. So when you're just walking around, this will be a good tool. The 100-400 is really good for just being capable, reasonably fast in good light, ok IS which every bit helps, and it has great optics.
If you're going to approach it like a bow hunter, then consider the advantages of the prime. I do not at all discount the difference between F4 and F5.6. To me, when doing wildlife, that is big. When birding, that is big. Especially when dealing with light that is not ideal, and dealing with backdrops that are not ideal. If you're going to be patient, study, stalk, prepare and be in a location for your subject, this is a great tool as an alternative to do a different kind of shot. I would use the 300 F4 naked, for it's aperture & speed. Adding a 1.4x TC is great when you really need the extra pixels on target and can be ok with aperture loss. I would not get it with the intent of always using a TC. I would simply include a 1.4x TC as an option for when things are just very distant and a few more pixels make the difference for you. Otherwise, I would consider the 300 F4 as naked lens and use it that way to keep it's advantages. IS is very handy, but you can get the non-IS for considerably less and it's worth considering for a budget approach to really good telephoto birding on APS-C.
You also need to consider size, weight and overall ergonomics. You'e had a long lens in the past and didn't bother with it (500mm). Ask yourself why? Will you do the same thing with a 400mm? Will a 300mm prime be small and light enough that you are more likely to actually use it? Lots to consider here, because all the great properties in a lens in the world is moot, if you won't actually pick it up and take it out and enjoy it from a physical aspect.
In the same sense, a 150-600 flavor may also be worth considering. It's bigger, heavier, and longer. But, it's an end-game long lens to relax and shoot with from a seat if you want, or a blind, best used on a tripod and just take your time with things. You can get one for $700 these days, here in the POTN forum, about the same cost as a 100-400. And for small birds, deer, etc, I would get one, with better stabilization, more reach, etc. Worth considering. But again, you had 500mm before, and you got rid of it, so there's something to think about in big lenses. Maybe you would be happier with a shorter, smaller lens.
One thing to remember, is what will you gain over a 70-300 VC. You can gain AF speed, aperture, overall sharpness. But at what cost is it going to be worth it to you?
Very best,