I have not gone into this at all, but my initial thought is that as long as every log entry also have a unique id of the last log entry at the time of it's writ

I have not gone into this at all, but my initial thought is that as long as every log entry also have a unique id of the last log entry at the time of it's writing, you can always piece together a deterministic log without any locking or voting. Just share everything you know.