Wrap It Up
Once you've got what you think is a working backup, you unplug the main drive, plug in the SATA backup drive and a LiveCD, and change the volume name to the regular volume name for the main system.
In the example following, terrarium is the main drive volume, and terrarium-back is the backup (change these names to fit the actual ones on your system). For example, do not use
# vgchange -ay
before renaming an LVM volume
# vgrename terrarium-back terrarium
After it boots, go back to the Knoppix LiveCD and rename it with whatever backup volume name you used in your backup scripts, so that you can back up to it. Once you know the backup works, you're done.
Enjoy your new, faster, hard drives, and the security of knowing you've got a working backup as well.