How to redirect outbound traffic to 2 ISP links

instead of transparent monitor, you can simply create ping icmp monitor with isp router's IP specified in it.
create that icmp monitor for each isp router that you want to monitor then bind that monitors to any relevant pools.
ensure that your fwrouter properly routes above ping traffic.

most ltm and gtm implementations are indeed behind NAT gw, i.e. f5 device doesnt hold the public ip address.