Internal RAID drive not searchable
Finally, an answer! I contacted Apple Support with the problem soon after I made this post. Two weeks and many hours of phone and chat support later, we seem to have found an answer. The problem appears to have been with the indexing at the root level (which is why reindexing from System Preferences didn't work), likely caused by the macOS 10.12.4 software update. The solution was simple:


Disable all backups (Time Machine, Carbon Copy Cloner, or similar)
Open the terminal app and execute these three commands in this order:

sudo mdutil -i off /Volumes/Server\ RAID/
 sudo mdutil -E /Volumes/Server\ RAID/
 sudo mdutil -i on /Volumes/Server\ RAID/


Following this, the mds and mdworker processes get right to work reindexing (spotlight shows reindexing progress).