One Port, One Computer: The problem is that my router settings will only let me forward Port 8333 to one IP address (or computer). It will not let me set more than one IP to forward to the same Port 8333.
An explanation of port forwarding is in order. When you say IP address here, you're referring to
private IP addresses (reachable only from your LAN, not the Internet). When other people connect to your Bitcoin node, they are connecting to your
public IP address, and you only have one public IP address (that of the router). As a result, all incoming connections end up connecting to your router, not any of your computers, which obviously isn't what you want. This is where port forwarding comes in. With port forwarding, you tell your router that connections to your public IP on a particular public port should be forwarded to one of your computers, on a particular private IP and port.
Now, it is nonsensical to try to forward a connection to two computers simultaneously. If you did, the client connecting to you would receive two simultaneous responses to each request, and fail hilariously if those responses conflicted in even the most minor way. It won't work at all, and any sane configuration software won't let you try. Thus, if you have two computers accepting incoming connections, they
must use two different public ports, so that the router can know which connections go with which computer.
The bigger question is,
what are you really trying to do? Running two Bitcoin nodes on a single public IP is a strange configuration, and I'm not sure how such a configuration would be useful.