To me, it seems like your team isn't that good at judging ability. To compensate, you rely on coding questions. This what the industry has been doing for years. What exactly is innovative here? I see the need for coding questions (and think that your method sounds pretty good) but too often culture fit & 'soft skills' are overlooked in favor of cramming as many technical questions as possible.
One of the best experiences I had on an interview involved no coding on-site at all. I completed a project for them, they liked it, I got an interview. 3 hours of culture/team/work philosophy. There were no surprises - if I wasn't "technical enough", I wouldn't have been let in the door. It took time up front, but at least the interview itself wasn't waste of time, PTO, and money.