write an irule to route (not re-direct) the traffic to an URI instead of a pool.

I would not proxy this type of configuration. Instead of having the F5 resolve and proxy, I would redirect the client. This way, the client can then use their DNS to resolve closest resource and continue with the connection to the resolved IP address. Otherwise, you may end up with higher latency. User is West Coast, accesses an East Coast instance of F5/NGINX, and then is proxied back to West Coast. Makes no sense. Distribute the load balancer, and have client redirect to best DNS resolved resource.