How about going the other way and fully commenting the config, sending it to them and asking them how they would implement all of the things that you are using in HAProxy in nginx.
If they pass it back to you as "that's your job", then you can reasonably ask them that as you have a working solution in HAProxy, would this not be a waste of resource ? You could even suggest that it might be better for the organisation to move to using HAProxy instead of nginx for its advanced reverse proxy and load balancing capabilities.
