Every popular website will go through Eternal September at some point: https://en.wikipedia.org/wiki/Eternal_September

The challenge is how to enforce quality despite the surge in users.

I had never heard of that but did notice the effect.

A required lurking period, maybe?

Unlikely to work. Required lurking means lack of participation and thus lack of learning.

My counter suggestion is to encode the culture you desire in to the function of the site.

Medium was originally invite only, so the earliest articles on the site did indeed have a certain amount of importance and quality to them.

Unfortunately, since it opened up to the public, it's turned into something akin to a cross between an inspiring cliches platform, a marketing tool and a place for people to complain about things on social media sites.