Hi Jeff,
Welcome to the F5 world :)
You can use a 0.0.0.0:0 all protocol virtual server (forwarding if you want to use the routing table or performance layer 4 with a fastL4 profile if you have multiple gateways you want to load balance between) enabled just on the VLAN the clients are on with SNAT enabled. LTM will then accept any connection in on that ingress VLAN and route the traffic out with source address translation. You might want to use a SNAT pool if you have a lot of active connections. This will help avoid port exhaustion.
If this sounds right and you want details on how to configure this let us know.
Aaron