My workaround for this seems to be working (although it is less than ideal).
I have a scheduled job that runs every hour to rsync my calibre library to a copy on the NAS. I then use Synology Drive to sync this copy to my PC so I can use the PC version of Calibre on a fairly recent snapshot of the library to sync to my Kindle. I found several examples of where people have reported Synology Drive doesn't properly detect creation/modification of files but with no clear solution (other than using alternative tools), so it sounds like I need to get rsync working from NAS to PC - there's my next challenge