You should be able to forward on the Syslogs from SolarWinds to another system and tell it to "Retain the original source address of the message"; by doing this I think you will essentially be accomplishing your "unfiltered" goal.
To do this all you need to do is go setup a syslog alert for all logs and for the Alert Action choose Forward the Syslog Message where you will have a check box to retain the original source address of the message.
Hope this helps!
Thanks Byron, That did answer my query. Appreciate it.