I've also used DMS to migrate smaller datasets (~200GB) from AWS RDS MySQL 5.7 to RDS PostgreSQL 11. 10 seconds of downtime here was actually incurred not due to the migration itself, but to enable MySQL binary logging on the RDS instance, which requires a restart, and which AWS DMS uses to replicate changes from the replication source (MySQL) to the target (PostgreSQL).
Traffic was steered to the new PostgreSQL instance not with DNS/Route 53 weighted records, but an application-level percentage enroller (based on user ID). Our particular set-up did in fact have apps talking to both databases simultaneously, each with a percentage share of traffic, and so we did not need to incur additional downtime to cut off traffic to the original source database - though now you do have to worry about eventual consistency.
I wouldn't recommend using their Schema Conversion Tool. We instead migrated the data as 1-to-1 as possible into the PostgreSQL target table, and then used plpgsql triggers on the replication target table to clean/validate the data and write it to another table with our desired (and more strongly typed - no more storing JSON as TEXT) schema.
There were also some issues with the replication task seeming to stall and stop during the change data capture (CDC) phase. As mentioned support is kind of spotty in this area, though we learned it may have to do with sizing the DMS replication instance correctly.