Hi Tom,
For minimal downtime, you could build your new cluster and then add a node as a slave to your existing host, sounds like that's your plan. This will then allow data to flow over to the cluster. Once your happy it's replicating ok then do an orderly switchover and forget the original master. Downtime is maybe 10 minutes on a slow day depending on what effort to repoint your application layer. Also, you can probably bring up a single app node initially much quicker and add your remaining nodes more leisurely. Allows you to check for errors on your app layer through a single node and control things
I would use Percona Xtrabackup to make our backup. It's much quicker and I found much better to MySQLDump unless it's presently only a small database. Will also carry over your GTID etc for sync. I have some notes on my blog on my switchovers
Cheers
Peter