I think your premise is wrong and you're vastly overestimating the value of work done outside of your job.
- Having side projects: I was never asked past internship interviews. Even interviewing for my first job after graduation, I talked about what I did during my internship, not about side or school projects.
- Meaningful yet small contributions to open source: I don't remember anyone noticing nor asking.
- Major contributions to a big open source project: I assume these people get hired easily.
Recruiters are not dumb. They know that most good candidates are either not allowed or not willing to work on meaningful projects on the side, outside of a few very specific cases. Don't waste your time with companies that have delusional hiring standards.