Thr overtime pay depends on the company. Mine gives us the equivalent overtime hours in days off.
So that gets close to Game Design! Being able to draw out your ideas and concepts is a huge plus. In my company, we have Game Designers that are focused on balance, but that's not all they do. Being a min-maxer can help you as well, since you may have an idea how to bring min-maxers to play your game (they're valuable!)
It is pretty hectic but like I said, it was only about very specific parts of For Honor. The game designers puts out ideas and numbers, and I put them to the test. Then I give feedback to the Game Designer, who will make changes to his numbers according to what I've said. I need to give him clues and solutions on the problems I bring up (ex: Boss keeps blocking every attack, make him more vulnerable to guard breaks)
For that kind of writing, you might be oriented better as a Mission/Quest Designer than a narrative designer. The overall story doesn't really matter, but empowerement through player actions is the kind of narrative Mission Designers will create.
I went to school and took a Game Design class, but I am now doing something else entirely, focused on programmers, and I love it!
Starting a company without having worked in the industry can be insanely hard, in my opinion you should take a course and find a place in the industry, then with your experience start your own company :)