@malnpudl mentioned "The Moth," but what this reminds me of is the old Fray-day events back in the late 1990's (before Zuckerberg and Google ruined everything.)

These were community storytelling events, but the organizers always preloaded the reader queue with good storytellers. What I learned from those is make sure you have drafted 2-3 people who you know will have good stories, appropriate for the audience, and that will set the expectations for others.