Moving data is always the trickiest part! We get a lot of Heroku customers who need help with their data migration. My honest answer is there will always be some downtime while the switch over is happening, but we know of a few ways to reduce it. Unfortunately Heroku PG databases don't allow outside replication setup, so we can't really baseline your data and then close the replication gap with a shorter downtime. But we do support multi-DB solutions so we can run against an old and new DB at the same time while data is gradually being moved over. If you're interested, ping me at hello-at-cloud66.com if you want to discuss further :)
