Hosting Multiple Servers on the Same Port on a LAN

Let me preface this by saying that I think I have a resolution, I'm simply trying to confer with the community on if my understanding is correct.

What I want to do: I want to host multiple web servers on a number of different servers behind a router, all on the same port.

The solution I've arrived at: Have a forward-facing server with port forwarding of port 80 to itself. On this server, a series of http-proxies, configured like so:

<VirtualHost *:80>
    ProxyPreserveHost On
    ProxyPass        "/" "http://other.lan.server"
    ProxyPassReverse "/" "http://other.lan.server/"
    ServerName website.com
    ServerAlias www.website.com
</VirtualHost>

After placing website files on the other local server that does not have port forwarding, I then set up a virtual host config that actually serves the website from other.lan.server.

It's my understanding that the port-forwarded proxy server will forward to other.lan.server, find the appropriate host on that server, and forward that request back to the proxy, which will then serve the website externally.

Is this correct?