How to config PBR

In case you want to use the proxy to forward the client requests to the public internet, it will be necessary to allow traffic from the proxy IP address on the firewall ACL. In case you use SNAT on your forwarding virtual servers, the SNAT address used by the load balancer needs to be permitted on the firewall ACL (as it is replacing the original client IP address or the IP address of the proxy - both are the source IPs).

In case no SNAT is used on the virtual servers, it is necessary to create routes on the ISP router to make sure responses from the internet will be routed back properly to the proxy or to the client by using the floating self IP on northern interface of your BIG-IP as next hop.

Is the tcpdump showing something, if you try to get traffic on port 80 through the BIG-IP?

Would you provide us the output of the following, please:

tmsh list net vlan
tmsh list net self  
tmsh list net route  
tmsh list ltm pool  
tmsh list ltm virtual