Zero-downtime database migrations with read replicas — cutover strategy

We're planning a major schema migration on a PostgreSQL cluster with 3 read replicas. Current approach: stop writes, run migration, resume. Downtime ~2-3 min. Looking for proven strategies that keep the system fully online. Specifically: how do you handle FK constraint additions, column renames, and backfilling large tables without locking? Tools used: Flyway, pg_repack. Curious about patterns like expand/contract, shadow tables, or logical replication-based cutover.