My journey up from Senior/Staff was mostly on the back of proposing and then leading cross-functional projects.
Which means I was doing Principal work before being granted the title. To be honest it was (and remains) a huge amount of work and I wouldn't continue doing it if the recognition and compensation hadn't been forthcoming in the following perf reviews.
If you are doing this stuff and aren't moving up where you are then you should be going somewhere else as that is probably a very exploitive work relationship.