The issue you are seeing when linking a reverse proxy to a web adaptor to ArcGIS Server is a known limitation when the context name is different between the reverse proxy and the web adaptor. As you have already mentioned, the webContextUrl parameter for ArcGIS Server is only applied when there is no web adaptor in the configuration. The two solutions I can think of are ones you have already described.
1. Remove the web adaptor from the configuration and specify the external url in the webContextUrl parameters in the ArcGIS Server Admin API. This matches this configuration:
Clients - Reverse Proxy 1 - Reverse Proxy 2 - ArcGIS Server.
2. Install a second web adaptor called 'accesspoint' and configure your reverse proxy to redirect to the 'accesspoint' web adaptor url to access ArcGIS Server. You can leave the 'arcgis' web adaptor in place if you'd like or uninstall it. It won't impact ArcGIS Server having multiple web adaptors.
Hopefully one of those will work for you.