I like your "tell me about a time when" approach,[1] and I've used it successfully in the past, but I've never seen a good way to formalize it. Have you ever been able to delegate that responsibility to a team of other people and get results more or less consistent with what would have happened if you'd conducted all of the interviews?
My current opinion is that while it's effective, it means there's a significant bottleneck (sometimes a single person) for the hiring pipeline. i.e. you still need at least one earlier tier of interview to winnow the candidates down to a volume that's manageable for the bottleneck, and the earlier tier needs to be something more standardized that can be delegated to a larger group of people. i.e. "can this person explain common technical details A, B, and C of work in this department well enough to demonstrate solid understanding?"
[1] I read years ago that border guards in some countries use a similar technique, because if someone is being deceptive, it's unlikely they can handle a random walk to an arbitrary depth of detail.