Presumably you would only hire people for a very high level, very well compensated role, and those individuals would plan on staying for a decade or more?
I'm not saying your process wouldn't be effective, but it is asking for a very big commitment for one interview for one position at one company. (And that same commitment would have to come from your company and all the interviewers involved!)
Not sure why I understand why this is a big commitment. The first two steps (manager call and a tech interview) are already happening. I'm changing the onsite to exclude whiteboard programming and do real hands-on keyboard programming plus code reviews and presentation which are all things that an engineer is expected to do.