Reclaiming occupied space
Turns out the answer came out of left field. I had done a Spotlight rebuild, which didn't reclaim the space, but what it did do (I think) is change totals in About>Storage>Manage. The System went down to 90GB (which is still high but better), but Mail jumped up to 95GB. That gave me the clue to look in the ~/Library/Mail folder. From here it gets weird.

Turning on 'Calculate folder sizes' in the Finder, it calculated the Mail folder as 24GB.  However, underneath that folder were several "mail container" folders, one of which was 37GB besides another that was actually 24GB. Literally it didn't add up.

Inside of that 37GB folder was a Drafts mbox was 37GB all by itself!  

Over in Apple Mail, she had no visible Drafts folders in any of the three accounts. I checked preferences to make sure each account was pointing to a server Drafts folder, and they were.  And when I created a new draft, it showed up properly.  So, the functionality was fine.

So, I figured out which Gmail account this huge Drafts folder belonged to (by watching the timestamps on the folders when I updated in Apple Mail), and then logged into that Gmail account via web. There I found a Drafts folder with hundreds and hundreds of emails with attachments (its normal for her to work with large PDFs).  These Drafts weren't getting deleting when she sent them.  So, I cleared all the Drafts off the server.  However, when I later launch Mail, the "cleanup" I was expecting didn't happen. Somehow, the Drafts mbox was a separate copy of these abandoned Drafts.

So I was left with quitting Apple Mail and Finder-trashing the 37GB Drafts mbox.  Even though the ~/Libary/Mail folder didn't gain any space, the overall hard drive free space did (as well as About>Storage>Manage).

She's got enough free space to work with now, but System still shows as 90GB and we don't know how she got into this predicament in the first place.  So, we don't know if this is the end of the saga.  (Perhaps because she travels a lot, she's "offline" a lot and Gmail is being ultra conservative saving her Drafts?) I suppose when she's back from her travels, I'll zap that email account and re-enter it, so it can download a fresh copy from the server.