Author here. You can move the sqlite database to a separate location by setting a variable, and that should resolve the syncing issues. I do this and have the files synced via Dropbox across my different machines.
I tried storing the db in a shared Syncthing directory, but I had to make sure I only had one copy of Emacs running on any given machine. I of course couldn't do that so I would get conflicts with the db file and have to manually clean it up. Did I miss something?