Can traffic exit 1 VS and re-enter through another? A TCP pull routing question

I'm in the process of configuring a TCP pull from my internally connected pool member servers out to external clients, and I'm a bit confused on how to get this traffic to pass through correctly. Is there a way to have a single VS handle the outbound connection establishment and inbound data receipt while still load-balancing the incoming traffic, or does this need to be achieved by 2 separate VS?

Technically, the F5 is inline (relative to the pool members and the data feeds/sources), but it may be important to note that the F5 internal self-IP is NOT the default gateway of the pool members (it is just another IP on the shared data landing area VLAN).

So far, I've initially managed to receive this traffic via a configured forwarding VS for the specific outbound path and port, but ideally I'd like to have the incoming data be load-balanced between the pool members, rather than coming back through the forwarding VS as it seems to be (which is also confusing, wouldn't a targetted forwarder be unidirectional?)

Appreciate any insight.