In order to avoid spending time re-writing the command line application, it seems to me that all we need to do is to look at the timestamp of the sqlite3 file (I assume all machines will be withing a minute or two of each other). This isn't very future proof, but it minimizes your expense.
That being said, what remains is for us to put together an MDNS server to broadcast the availability of a file service using node.js which will distribute the most recent copy of the sqlite3 file to all machines.