When you move the partitions around, in addition to editing grub.conf and /etc/fstab, you will probably need to create a new initrd as well.
You DEFINITELY want to have a copy of Knoppix on hand during this procedure. For one, to tar up the partitions in preparation for copy as Brian1 said. But also to rescue yourself if you get something messed up. Backup you existing partition table before modifying it, so if the stinky stuff hits the rotating device, you can recover back to square one and start over.