I dunno, I've personally spent on average half a day (3-4 hours) with on-site interviews as a candidate. When on the other side of the table, it's been about the same (~3 hours). With a tractable enough problem, I think you can fit it into a half-day. You could also begin the design/research process as part of a phone screen, have the candidate further prepare on their own time, and then present/discuss as part of the on-site, along with the more in-depth technical stuff.

After you've run this process enough times, your interviewers will have a good grasp on the various solutions and technical problems. Most people's training on how to interview comes from how they themselves were interviewed - which was probably poorly done. Improve the interview process and you can train people to be better interviewers just by being interviewed. :)