This is too complicated. With a load balancer, the backend hosts don't need to exist in DNS, and the backend hosts don't even need a globally unique IP address. They can sit on 10.0.0.1 and 10.0.0.2 and have fake hostnames.
What matters is that the servers on those backend hosts greet and respond to the client with a public DNS name, and in particular, that they present a certificate for that public DNS name. In this light, it is natural to give the proxy host the public DNS name and IP address, because that is the only name and address that matters to the client. Wietse