How to rewrite / proxy an Apache URI to an application listening on a specific port / server?

They say that Apache's mod_rewrite is the swiss-army knife of URL manipulation, but can it do this?

Lets say I want to add a new application to my Apache webserver, where the only configurable option of the app is a port number.

I want to use & give out URLs of the form "http://hostname.example.com/app" rather than "http://hostname.example.com:8080". This would ensure that clients would be getting through the institution's firewall as well, and it's generally tidier.

My application includes absolute URIs in php, javascript and css, so I want to prepend my own root location to the URI in the applications internal links. I have no access to DNS records and so can't create another name-based virtual server.

Using Apache's mod_rewrite and mod_proxy modules, I can transparently redirect a client to the correct home-page of the application. But links within that homepage don't point a client to links relative to the new base URL.

So, what's the best way of proxying a request to an application that is listening on a specific port?

For example, if I had an application listening on port 8080, I could put this in my Apache configuration:-

<VirtualHost *:80>
    SSLProxyEngine On
    ServerName myhost.example.com
    RewriteEngine On
    UseCanonicalName On
    ProxyVia On
    <Location "/application">
        RewriteRule ^/application/?(.*) http://localhost:8080/$1 [P,L]
    </Location>
</VirtualHost>

This would work fine if the application didn't use absolute URLs, but it does. What I need to do is rewrite URLs that are returned by the application's css, javascript and php.

I've looked at the ProxyPass and ReverseProxyPass documentation, but I don't think these would work..?

I've also come across Nick Kew's apache mod-rewrite port mod-proxy