Manually replicating writes to all nodes seems pretty fragile. At some point you're going to run into classic distributed systems issues, like netsplits, and reconciling the latest count. Maybe a CRDT implementation would avoid these issues alltogether?
But it sounds like LiteFS (with a single writer?) might be a pretty nice setup if it handles replication for you, as you probably don't want to build a Raft or Paxos system yourself.