An active github/stackoverflow account would definitely have helped me, but it seems like, those things just gets you to the first step of getting a phone interview. You will still have to go through the entire process. But yeah, I do just have to keep at it.
If you're talking about a company that's been around a while and has a big HR department, they're going to have a well-defined interview process, and you'll be playing by their rules.
A smaller company or a startup is more likely to be flexible, and you may be able to suggest that they give you a sample project to start. They may prefer this, as they don't have to pull an engineer off an active project to spend time interviewing you. Everyone is different, so if they don't like the suggestion, you may have to work with them.
I saw from another commenter that you are practicing your skills at working with someone. The time and energy you invest in your people skills will pay off in a lot of ways over the course of your career (and in your personal life), so it might help to think of this as an opportunity.
FWIW Here's my company's project (bottom of the page) http://cloudspace.com/hiring/