Replica replay lag climbing

It's 14:10 and PagerDuty fires: "read-replica lag > 90s" on your Postgres fleet (1 primary, 3 streaming replicas) backing a social app. Users report stale data, they post a comment, refresh, and it's gone for a minute. The lag dashboard shows replica-2 and replica-3 climbing steadily to 180s while replica-1 is fine. Primary write TPS is up ~40% since a marketing email went out 20 minutes ago. pg_stat_replication shows write_lag near zero but replay_lag ballooning; the replicas' CPU is pinned at 100% on a single startup/recovery process. Disk and network on the replicas look healthy. How do you triage and mitigate?