Integrating HA with other web domains hosted on same server

Are you running apache by any change?
If so, you can use apache as proxy forwarder…

I myself run http on my own web server and HA on https (proxy forwarded)
So port 80 and 443 are both forwarded to apache; from there 443 is forwarded to HA 8123 (just http as the certificates reside on apache)