In the end, it ended up not being too difficult to do. Just time consuming. Or maybe I was so worried about it, it just seemed less of an issue. 
This is what I did:
1 - Install PMS on the Synology using the PlexPass package.
2 - Start PMS and do the basic configuration, but without adding any folders to any library. Make sure to disable empty trash and automatic library updates while doing this.
3 - Stop PMS on Synology
4 - Stop PMS on Mac
5 - Transfer files from Mac to Synology (this takes a long time)
6 - Create tarball from all files under ~/Library/Application Support/Plex Media Server/, but excluding the “Plug-ins” directory
7 - Convert ~/Library/Preferences/com.plexapp.plexmediaserver.plist to readable format by executing plutil -convert xml1 com.plexapp.plexmediaserver.plist
8 - Open com.plexapp.plexmediaserver.plist and look for “MachineIdentifier” and “ProcessedMachineIdentifier” entries and copy value to temporary document.
9 - Transfer tarball from Mac to Synology
10 - Extract tarball into Plex directory on Synology. Path is dependent on where Plex was installed, in my case /volume1
Added 5/29:
10a - Execute chown -R plex:users . from inside the Plex directory
11 - Open Preferences.xml under [PATH_TO]/Plex/Library/Application Support/Plex Media Server/ and look for “MachineIdentifier” and “ProcessedMachineIdentifier” and change values to the values previously copied from Mac into temporary document.
12 - Start Plex on Synology
13 - Open Plex in web browser. All content from your old library should be there
14 - Add new location to each library section. Do not remove anything yet.
15 - Update library sections manually. This will take a while.
16 - When fnished, check if all looks ok
17 - Go back to library sections and remove all old obsolete entries leftover from old machine
18 - Update library sections again.
19 - Turn on empty trash and automatic updates (if desired)
20 - Enjoy Plex on Synology as if it always had been running there.
