Ok, we had a MySQL DB around 500GB, and not on Heroku, but we used the AWS Database Migration Service:
https://aws.amazon.com/dms/
We had just a few minutes of downtime.
I did have few issues around permissions, but an AWS support person walked me through the process and we got it up and running. The support was great, and we just have standard business support.
EDIT: DMS might be a no go, as jpatokal points out. While Heroku allows external connections, it doesn't allow super user access which, AFAIK, DMS requires.
Heroku Postgres doesn't support external replicas, which complicates migrations out considerably. If you can't tolerate more than a few min of downtime for writes, you pretty much have to build the replication at the app level.
We had just a few minutes of downtime.
I did have few issues around permissions, but an AWS support person walked me through the process and we got it up and running. The support was great, and we just have standard business support.
EDIT: DMS might be a no go, as jpatokal points out. While Heroku allows external connections, it doesn't allow super user access which, AFAIK, DMS requires.
https://devcenter.heroku.com/articles/heroku-postgresql#conn...