I managed to do it quite easily:

instead of sending logs to the local syslogd, I'm sending them directly to remote server (using logger).

As simple as that:

I changed that line CustomLog "|/usr/bin/logger -t S06_access_log -p local6.info" combined

to: CustomLog "|/usr/bin/logger -n $REMOTE_SERVER_IP -t S06_access_log -p local6.info" combined

maybe it'll be useful to someone