F5 VIP listens on udp port 514 and forwards to all servers in pool

You could simplify this even a bit further by placing all (3) pool members into a single pool and switching from the default distribution of 'adaptive' to 'replicated' for your Log Publisher Destination combined with following iRule.

when CLIENT_ACCEPTED {

  set hsl [HSL::open -publisher /Common/syslog_publisher]

}

when CLIENT_DATA {

  HSL::send $hsl "[UDP::payload]"

}