I'm unsure that I understand the path you've undertaken to attempt to resolve this issue. If you're using the web adaptor, the web adaptor will proxy between the external facing ports 80 and 443 to the GIS Server on ports 6080 and 6443. No NATting/port mapping/redirects are required in that sense. What you've done is ship incoming requests to the GIS Server, running on port 6080. None of the documents in the screenshot above are hosted on the GIS Server - they're all hosted on your IIS instance.
The first thing you need to do is undo the port mapping you've set up at the router end (from port 80 to port 6443). By setting that mapping, you're bypassing your web server entirely. Ports 80 and 443 on the router should translate to ports 80 and 443 on your IIS web server. The web adaptor will handle proxying from the web adaptor instance (called ArcGIS) to your GIS Server.