Ah, the extra info makes it a completely different situation! I'm sorry if I came across as patronising, but from what you said, it seemed you were asking how to configure a simple one-webserver setup with multiple hosts, and I couldn't really see the issue... so (wrongly) assumed you didn't quite understand something.
There is definitely nothing within a consumer router that would allow this type of setup. Not sure how VRF works (in fact I had to just look it up to see what it was lol)
What apache CAN do is reverse proxying though. So the way I could see your setup working is this:
All web requests are port forwarded to one of your web servers. On this server you need to confgure a virtual host for each domain you want to deal with, and instead of specifying a document root, you specify using ProxyPass and ProxyPassReverse directives which internal address that requests for this domain name will get forwarded to.
Reverse proxying can coexist with a normal webserver on the same machine, which means you don't have to set up an extra machine just to deal with this.
I have never set this up myself, but it looks reasonably straightforward, and there's tons of information on the net about setting it up.
This page looks reasonably useful, although I just found it by googling, so it might be a load of rubbish! At least the term reverse proxy gives you the right thing to search for
Good luck