Was just checking it out, in my quick test actually serving HTTPS on port 80 does not seem to work with Public Device URL (while in general it works, could serve it on the local network). So that workaround is probably out, then 
If you’d like a tunnel that is completely independent of resin.io, then maybe can recommend ngrok. That’s a pretty good service that we are using for a bunch of times here and there (not in the platform itself, but for projects). That way you can create your own separate communication channel, and seeing their docs, there seems to be a couple of settings that are relevant to how to do a setup as you mention.