We solved the issue by addling the appropriate line to the syslog config file in the underlying OS.
Now all syslog messages OS and AirWave send on to the master syslog server.
Will future updates of Airwave overwrite that configuration file?
We need a single central syslog server for PCI compliance, so this is actually an ideal solution for us -- worried now about possible ramifications of meddling under the hood...
--Matthew