Just wanted to let everyone know that I did the surgery and everything went fine aside from a couple of minor hiccups. The NAS is back up and running and all the data was preserved. Here are the steps I did in case anyone else needs to do something similar.
1. Back up everything important to external storage or cloud.
2. Shut down and back up VMs from Virtualization Station to a shared folder.
3. Back up system config via Control Panel.
4. Select "Safely Detach" for the TR-004 enclosure in the External RAID manager. Shut down the enclosure once that is done.
5. Select the main storage pool in Storage & Snapshots manager and do "Safely Detach" as well. See
this article for details.
6. Shut down NAS and remove all the drives, then power it up, log into QTS and do "Reinitialize NAS" via Control Panel.
7. Once the NAS is restarted, use Qfinder Pro to set up the NAS. Format SSDs as RAID1 and let QTS use it as the system volume.
8. Log in and restore the system config from previously saved file. (I had a problem after this, where the QTS would not respond on usual ports, but I tried resetting (holding the reset button for 10 seconds) and the restoring from a slightly older system config backup and then it worked.)
9. Shut down NAS, insert all the drives and boot it back up. Go to Storage & Snapshots and do "Scan and recover storage space" on the NAS. The system should recover the storage pool and volumes. (Another small issue was that the QTS complained about duplicate shared folders (Public, Web, etc). I should probably have deleted from those before detaching the storage pool.)
10. Power up the TR-004 and do the "Scan and recover storage space" again.
11. Reinstall the necessary apps. Start up Virtualization Station and recover the VMs from the backups.
That's pretty much it. Note that you may have to delete and recreated the shared folders to point them at the proper storage pool (since the underlying pool numbering probably changed).