The machine won't boot without that hard disk, unfortunately...and, the acronis forums, the best advice I can seem to find is "move the hard disk to an external dock to clone." All my SATA ports are hot-swap enabled, and I did move it to a different channel, with no luck. The other thing they recommend is backing up the drive to an external drive and restoring the backup to the new drive...but, I don't have anything big enough.
I will try to move the MBR using the repair solution this evening, and I'm crossing my fingers that after that, I really can just drag and drop all the files, and rename the drive. That said, of course, it has lots of programs installed to it, so I get a little worried about the connections.