Love seeing the love for SQLite. Personally, I've had a great experience with litestream, which will continuously replicate any changes. Are you using https://sqlite.org/rsync.html?
For example I have a sqlite db in my userdir on most servers I (personally) ssh into with "things I'd like to remember" (using dnote for spaced reptition). When I make a change to that file using "dnote", sqlrsync waits until changes stop, performs the sqlite3_rsync, and Cloudflare sends a websocket message to subscribers of that file (me on other servers) to pull down updates when they can.
I'd also like to add "dead man's alarms", etc. So it's bells and whistles around an easier-to-use sqlite.org/rsync.