If you have return traffic that goes direct from VLAN 200 to internal hosts, you will need to set up a second forwarding virtual server. The FVS matches destination traffic, and tells it how it is to be treated. With automap enabled, you are essentially talking to the server IP, and hearing back from the Automap address which will never work. Create the second forwarding VS as shown below where 10.x.x.x is your internal management network range. The LTM will match the MOST SPECIFIC virtual server to handle the traffic, therefore internal traffic will not use automap, but external will.
VLAN200-Forwarding { destination 10.x.x.x:any ip-forward mask any profiles { fastL4_stateless { } } snat none translate-address disabled translate-port disabled vlans { LAN-VLAN200 } vlans-enabled
Alternately, I think you could also set up an iRule to look for the destination address to belong to a group, and disable SNAT when the destination is in your group of internal addresses. That can be applied to the original Forwarding Virtual Server.