It was extremely satisfying to see the following dialog about the volume expansion when logging into my Infrant ReadyNAS:

The overall process of expansion took about four days, converting from four 320 GB drives to four 1 TB drives. (For reference, I selected the Hitachi 7K1000.B 0A38016 drive from ZipZoomFly, and did so almost entirely on price — despite my longstanding misgivings about IBM/Hitachi drives.)
The capacity expansion took longer than strictly necessary, because I wrote zeros across each of the drives before installing them, one at a time, in the ReadyNAS. (I ended up writing zeros to each drive twice, switching from the Disk Utility to the command line equivalent.)
Near the end of the process, I found out that the automatic X-RAID™ expansion doesn’t happen until you reboot the ReadyNAS after upgrading the last drive. I had also enabled a snapshot on the ReadyNAS, which also prevented the automatic volume capacity expansion, so I had to delete that.