If your goal is to influence the big picture at a corporation then your title probably has to be Sr. Director, VP, SVP, or something similar. Even then it won't be easy. Political and cultural inertia will conspire to prevent change.
What you need to do to break free is simple, but not necessarily easy - get a job with no technical requirements, but which has the potential for technical/cultural solutions.
This is the direction I eventually went in, and one thing I find interesting and notable is that even after solving all sorts of things through programming, people aren't letting me withdraw into just being a programmer - which I think is a good thing. Once I write a program to do something, then I have to document it, then I have to train other people to use it, and then we have to develop contingency plans to do without it if I should be hit by the proverbial bus. And maybe figure out how to get another developer up to speed to maintain it. If I were an actual programmer/developer, then all the different jobs would be pretty much left to other specialists and managers.
Maybe some people would say, just join a startup or make your own, and you will become more well-rounded, but I'm not swamped with offers to do that and have worked in larger organizations.