Not sure if I understand the configuration correctly. You say request is outgoing, but not forwarded. Probably all requests from the front-end machine get sent to the same relay. If this is the case, from the perspective of that relay, this is going to be just like any other PDU coming from any other peer.
With that assumption, I am sure that you can use Proxy-Info AVP for this purpose. Any downstream peer is required to return this AVP in the answer, irrespective of Route-Record. So at each node, the decision would be "if Proxy-Info AVP is present, if it is for me, let me remove and use it, otherwise pass it back in the answer". It will be incorrect for any node not to pass it back.