"Just buy a second controller and a dock"
So the solution to poor battery life is to spend £100. That's not a reasonable solution, that's throwing enough money at a problem that you notice the problem less.
How is the Vader 4 when it comes to compatibility with software like Steam? Is it recognised for what it is with full customisation? Failing that, does it have its own software that has decent customisation?
I use a DS4 with DS4Windows and occasionally also Steam for the strong customisation options. The last thing I want is to have to drop down to some bare minimum software, and there's usually not much online about how things like back buttons are picked up.