manual ip persistence

Have you tried "Least Connections (Member)" as the LB algorithm ?

If you explored playing around with LB algorithm, then you can try this - create 2 pools: POOL_APP_1 POOL_APP_2

Use an iRule that will send traffic from DMZ_Server_1-IP to POOL_APP_1 and the other DMZ server to POOL_APP_2

when HTTP_REQUEST {
if { [IP::client_addr] eq  } {
pool POOL_APP_1
} else {
pool POOL_APP_2
}