I've been having the same issues and I found an answer in the Binhex Documentation. Starting at Q24.
These are the steps I took using binhex-privoxyvpn as the container I wanted to route my applications through.
I'm using Radarr for this example. To start in privoxyvpn, I added port 7878 (Radarr's port) into VPN_INPUT_PORT. I then added a custom port with Radarr's port again, and a different port that will be used to access the WebUI. I just added one to my port and made it 7879.
I then set up Radarr as usual and added the --net=container:<container name> into the Extra parameters field.
After applying these settings, I was able to access my WebUI again through serveraddress:7879