Thanks! My goal is to make game systems that are simpler to use and make people's ttrpg experiences more fun.
As to your questions: The Quidditch rules are about narrating an exciting game of Quidditch at the table, not about playing a fair match between teams. (The game as written in the books is inherently nonsensical & unfair, right? A goal scores 10 points but the team that catches the one ball at the end gets 150 points? Ridiculous!) So keep that in mind.
Having a set number of rounds before you announce the Snitch is what I usually do. I'd suggest 2-3 rounds (where every player at the table has gotten a chance to roll during the match). But pay attention to your players! If they're having a blast describing all the cool plays & broom tricks they're doing, go for more rounds. If they're struggling to come up with new ways to describe getting the ball into the goal, introduce the Snitch earlier so you can move on to a more engaging part of the game.
Also note: Getting the Snitch requires a 10+, so it's statistically less likely to happen on the 1st try, which gives the opposing team a chance to steal. And the rules are written to allow player characters to be on opposing teams, for a player character team & a narrator-controlled team to face off, or even for all player characters to be observers who aren't on either participating team.
Hope that helps!