SNAT Persistence

I don't know if it is possible but maybe test if match across option does help.

https://support.f5.com/csp/article/K5837

Also maybe see if you can use two pools on one Virtual server or have one primary virtual server that redirects to the two other virtual servers:

https://clouddocs.f5.com/api/irules/virtual.html

You may also test this irule:

https://community.f5.com/t5/crowdsrc/snat-pool-persistence/ta-p/284232

I think we can create a datagroup that maps client IP to snat IP and apply an iRule to snat. 

1. Create SNAT datagroup

ltm data-group internal client_snat_map {
records {
192.168.10.34 {
data 10.1.0.7
}
192.168.10.35 {
data 10.1.0.8
}

}
type string
}

2. Create iRule and apply to the virtual server

when LB_SELECTED {
if { [class match [IP::client_addr] equals client_snat_map] } {
snat [class match -value [IP::client_addr] equals client_snat_map]
}