I think the most common issue with NAS or external drives is that, if the drives are allowed to spin down during idle times, and Plex tries to refresh metadata, oftentimes the drives don’t spin up fast enough. When this happens, Plex may fail to detect some files on the drive (because the drive isn’t up to speed yet), and assume they’ve been deleted. Plex then removes them from libraries. What you’re seeing doesn’t exactly sound like that issue, but it could be a factor. To prevent that scenario from happening, you should disable the “Empty trash automatically after every scan” option on your server:
Questions:
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When you said “No dice” after all the things you’ve tried, what does that mean? Did the new server not find the music? Did it catalog the music in the same “willie-nillie” way that the old server devolved into? 
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Are your files fully tagged with metadata, or do you depend on Plex to gather metadata from online sources? Is the “Prefer local metadata” option enabled or disabled? 
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Are you possibly looking at the library in “Tracks” mode, rather than “Album” or “Artist” mode? That seems unlikely, but, you know, sometimes the strangest things… 
The below comes from this How-To article:
Plex essentially has two ways to identify your albums:
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Folder/filename structure – If your files don’t have embedded metadata, or it isn’t accurate, or the “Prefer local metadata” option is disabled, the folder/filename structure of your music files must conform to Plex’s guidelines in order for Plex to accurately categorize your music. 
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Embedded metadata – for this to work, your embedded tags must be accurate (with some caveats, listed in the “Potential issues with embedded tags” section below). 
If you have accurate embedded tags, and you want to use the “Prefer local metadata” option, I recommend going through that How-To article and see if it helps. You might try it out on a few of the albums that aren’t being cataloged correctly.
