I haven't hired nearly as many as you, but I've interviewed dozens and have seen the same thing. This has been largely technical developer interviews, and the thing that seems to work is changing things up. We'll alternate between technical questions, coding challenges, and experience questions, and we tell them at the start that we'll take any questions they have at the end. If they seem overly stressed, we'll offer to take a small break (get water or something), especially since the interviews I'm part of are 2 hours long.

So far, it has worked well. We like the people we hired, and we give plenty of chances for candidates to redeem themselves during the interview if they give a stupid answer because of stress. We start easy and build up to harder questions.