Greg stepped me through it via jabber. Rough outline:
* Boot to Knoppix on the new system.
* Re-partition the new disk.
* Mount the new partitions.
* Copy the contents of the old system into a directory on the new system.
* Copy the list of modules Knoppix used to boot on the new system into the modules list on the new system. (IOW rely on the Knoppix hardware probing.)
* Reboot the new system.
That's glossing over a huge number of details, but anyone who knows a bit about Linux sysadmining could pore over the jabber logs and reconstruct a HOWTO. Who's got some spare time?