F5 HA Pair in front of DMZ IDS/IPS/Firewall Appliance

In addition to that, this setup is pretty much how the Link Controller would work or setting up links in GTM/DNS, where the traffic is initiated outbound from the internal network.

You need to make sure that the listeners (virtual servers) that you use are listening on the internal vlan and their pool members are the gateways leading or going to the internet, that way the connections are load balanced across the links outbound.

So pretty much just a reverse of your setup that accepts in-bound traffic. This is how this should work.