Can’t get External IP Address for RBR40 in AP Mode

if you do a tcp packet capture, you'll note that the orbi intercepts dns requests and responds to www.orbilogin.com with the IP address of the router.  Rather than dealing with a proxy server, have you considered trying to set www.orbilogin.com to resolve to your orbi hub IP address and see if that works?

I find it somewhat annoying that the orbi app doesn't let you specify the IP address of the device - what if you have multiple orbi devices on the network?  

I'm not entirely sure I understand your configuration though.  What's behind the proxy?  The orbi?  or the device you're trying to run the app on?  Is the application connected to the orbi (or one of it's satellites)?

One thing I've noticed is, using the ethernet backhaul on one of the satellites, the satellite doesn't appear to be capable of intercepting the DNS lookup for www.orbilogin.com and with the wired backhaul - in AP mode, connections through the satellite go directly to your router (the satellite functions as a separate access point) so the app won't work in that scenario.  If you're using a wireless backhaul your device has to pass through the orbi hub, which handles the DNS interception.  The workaround I have is I have the ethernet backhaul satellite wired into one of the orbi's LAN ports which is then connected ot the switch for the rest of the network.  So all traffic from devices connected to the orbi hub or it's satellite's pass through the hub.