First of all, thanks for taking your time and writing this very detailed answer.
I considered Unity in the past but I'm definitely looking to program in C++ and nothing else.
A little discussion about the lack of direct C++ in Unity:
Furthermore, I'd rather not learn a completely new framework which I intend to leave later.
I'm definitely not looking for the easiest option or something in the middle, I'm looking for the best one.
Difficulty is not a factor. I've got the time and the will to learn something new, I just need to know I'm on the right path before I dive in.
I'll try to rephrase a little bit.
Career-wise, would it be a wise choice to learn Unreal Engine 4 / CryEngine 3?
Would they open doors for me in the future, not only in the companies behind those engines?
Would any knowledge I gain from working on these engines be useful in other engines I might encounter in my career?
Would the experience add to my resume?
Alternatively, are there any other engines I should consider? Not because they are easier to get into, but because they seem like a good choice.