If I was assembling a new software team from a bunch of people whose resumes stuck out to me, I would invite each of them to bring some code to work on with me for 30 minutes. We'd pull up their code on a computer with a keyboard and mouse for each of us and just let the magic happen (or not). Rinse, repeat.
After those subsequent half-hours of coding with each of those people I would probably have a pretty good idea of who I would want to hire, just based on what they brought, how we got along, and (maybe) what we got done together. I wouldn't ask them a bunch of questions. I wouldn't ask them to write or read code while everyone else in the room watched. We would just be programmers together, doing programmery things.
If the field was still too large after that, round two would consist of random pairings of applicants and just let the magic happen (or not).
But...
Oh, well, yeah, you're right, it's totally impractical. We'll just go back to four or five rounds of painful back-and-forth questioning and whiteboard coding. Good call.