How to upgrade MySQL (5.5) production DB to 5.6 with minimal downtime
We used replication (no GTID) to replicate from our production 5.5 servers to our new 5.6 servers so to minimize downtime. Basically, set up your new 5.6 server to replicate from the 5.5 (cannot use GTID at this time). Dump 5.5 and restore to 5.6, start the replication.

When you move production to the 5.6 server, stop the replication from the 5.5 server . Reconfigure 5.6 server to use GTID (need to issue RESET MASTER and RESET SLAVE on the 5.6). Then configure your downstream 5.6 slaves.