Hello Frank,

It seems, you are using the mirror function of elog. It should resolve conflicts by itself acording to the documented rules. (https://elog.psi.ch/elog/config.html)
As I don't use this function, I can't say how good it works.

If you don't want to use this function, I would suggest using the "Execute new | edit | delete" feature to trigger a script after each change of elog entries.
This script could itself run "rsync" or your sync solution to make the sync and
should afterwards call "killall -HUP elogd" on the remote to let elog re-read the config (and this sould also update the indices)
(see Server Configuration https://elog.psi.ch/elog/adminguide.html)

If you have a sync-solution, which itself permanently observes folders for changes and syncs it by itself,
It should have the option to run a command after sucessful sync or you need an other method to call "killall -HUP elogd" after sync.

Personally I would recommend the mirror function as it has a internal conflict resolution.
I hope this helps.

Best wishes,
Sebastian

PS: I don't know anything about your setup, but maybe there is a solution, where you don't need the local servers.
As I think, the mirror function is mainly for backup reasons of a main server to a secondary one or similar.