How to speedup pg_dump big database
You don't actually have to dump to upgrade a PostgreSQL instance. For example, you can bring up a new cluster with access to an older cluster using the pg_upgrade command. If you're using XFS you can even use --clone. I would read the rest of the docs for pg_upgrade.

If you're just looking to move the instance you can try pg_basebackup - though I'm not sure that works across major versions.