Monday night I ordered a second drive from NewEgg to match the one already in my HP MediaVault. It came on Wednesday (way fast delivery!) and I installed it into the box.
After a little fighting with the administration tool, I finally got it set up as a mirror. I tried several times and kept getting either no response (either the page timed out or it just returned me back to the disk settings screen) or I'd get an error. I couldn't figure out what on earth was wrong. It is a brand new drive, shouldn't have anything on it. I didn't format it as the mirror is a block-by-block feature so it shouldn't require an pre-formatting. What finally worked was that I selected the new disk and chose "Erase Disk". The erase process only took seconds but I noticed a change in the recognized drive space. I then tried the mirror process again and it worked right away. None of the half dozen sets of instructions I read mentioned anything about erasing the drive first, but that is what seemed to be needed.
So now the main disk volume is in the rebuilding phase and should be done in some 12 hours. I feel better at least having a mirror of the data. The next step is to get a removable backup system in place. Fortunately, the MediaVault has USB ports to which you can connect mass storage devices. So I just need to get a USB hard drive or similar so I can back up periodically and safely store away.