Looking for suggestions to Migrate Amazon RDS Large Instance to non-amazon host - Live
Dump RDS and import it into mysql that holds all data in RAM disk:


Buy strongest possible EC2 instance that might hold your database in memory twice (you might prepare everything on a small instance and then ramp it up)
Create RAM disk, install and configure mysql 5.6 to hold both data and redolog on the RAM disk
Stop your db-using services, dump the RDS directly into the RAM-backed mysql
stop mysql, rsync the DB to a final place, kill the machine


You should do a dry run to estimate expected downtime.