BEFORE you wipe out your media on the NAS
Create a ‘Test’ Library and see how easily Plex can find and resolve those names. Doing so will have NO impact on your other library or media. It will be completely isolated. If it’s not right, wipe the test library from Plex, make the necessary corrections, add again (wash, rinse, repeat as needed)
Thank you for the offer but I do this because I enjoy it and teaching. Were I to spend a day performing the work for you, that would be different but you are actually solving your own issue. 
If you wish, you’re more than welcome to ‘like’ or whatever else you wish within this site as your thanks but FIRST let’s get it all done right
You’ve given me some of the best, most carefully explained, and responsive tech support I’ve ever gotten. Plex is lucky to have you here.
I’ll get back to you when I finish everything on my end. Thanks again.
Aaaaaand my Synology server suffered a volume crash last night. It will boot up but there are no volumes available, and each disk shows 0 kb used. I sent a ticket to Synology and was told “due to the increased volume of downloads of DSM 6.0 it may take 3 to 5 business days to respond. Thank you for your patience.” UGH.
But good news, I guess. This might not be a Plex thing after all.
Rebuilt the volume, scanned the drives, copied the data back over, set Plex back up aaaaaaaaaand … no further issues. This one seems to be the fault of an unstable NAS drive behaving unpredictably. Sorry Plex!
But a sincere thanks to ChuckPa for all your help!
