Is there a way to drain a ReadyNAS System

The RAID array is organized to evenly spread the data and parity blocks across all the drives - so the data blocks for a large file is saved on more than one drive.  The inodes/metadata are also spread across all the drives.  It's not structured like a book, where you can still read an individual chapter after you rip it out of the binding.  Therefore you can't migrate data one disk at a time.  

Also, the newer systems use a different file system.  You can temporarily migrate the disks o an RN300 or RN500, but to set up the new NAS you need to start by copying the data to another device.  Then set up the NAS, and copy it back.  

If you don't have much data on the NAS (e.g, if the volume is less than ~20% full) you could pull one disk out of the pioneer, and set up the new NAS. Then copy all the data, and migrate the other disks.  Otherwise you'll need to buy more disks.

What I suggest is to keep your Pioneer running, but convert to it a backup NAS.  

Getting there could be done with an RN516 and 3 new 3 TB drives (stealing 2 drives from the Pioneer), and converting the Pioneer to jbod when the data is migrated.  

But you'd be better off in the long term using larger drives in the newer NAS, and keeping slots open for expansion.  For instance, start with an RN516 with 4x4TB RAID-5.  That has the same initial volume size as the pioneer, but can expand  to 20 TB in the future if you need that.  Or 16 TB RAID-6.