I had a very similar problem. However, my problem was specifically that after you login to Webmin, it would redirect to the non-proxied address and port.
To further illustrate, assume I wanted webmin to appear to the outside post-proxy on 'https://example.com/admin/webmin', but it's really running on 'https://example.com:10000'. Going to the first address would display the login page, but redirect me to the second address (302 Moved Permanently). I could then type or paste the first address, and all would work as though I was logged in.
I tried following the directions on the Webmin wiki, your suggestion above, and various other suggestions. Then I found the solution. I needed to add another ProxyReversePass to my Apache configuration, to catch the URL in the redirect.
ProxyPass /admin/webmin/ https://example.com:10000/
ProxyHTMLURLMap https://localhost:10000 /admin/webmin
Of course, in /etc/webmin/config I have webprefix="/admin/webmin" and webprefixnoredir=1. I wanted SSL protection over my local LAN, so I left it SSL enabled and did the SSL proxy thing. Hope this helps as a possible solution to anyone experiencing this issue.
I was so desperate I was trying to modify miniserv.pl and even thought about breaking out mod_rewrite.