How do you handle freemium tiers when support tickets eat up 80% of your team's time?

Our freemium tier was meant to be our primary top-of-funnel acquisition engine. It worked too well.

Within six months, our customer support queue grew by 400%. Over 80% of our team’s time was spent responding to free users asking for custom setups and bug fixes, while our paying customers were waiting 24+ hours for an answer. We were giving away human support to users who had zero intention of ever entering a credit card.

How do founders restrict support scope for free tiers without creating a toxic brand reputation or completely alienating potential upgraders?