As BillBach said, don't use public IP's on your private side.
As far as how you would set this up. One solution is, for instance, a Cisco ASA device. A port can be used on your Private network as the gateway that your private addresses will point to. When a computer or device cannot find its destination on its own subnet it will route to the configured "private port" of the ASA. Inside the ASA you have Access Control Lists, outside routes, etc. If your "Outside Port" (a different port than your private port obviously) would, or could be plugged into your internet Router. If the Router is in Bridge mode, then basically any traffic coming into your 6 Ip addresses would be directed directly into the Public port of your ASA. In your ASA configuration you can (in logic terms)
If traffic comes in to Port0 ( your public port) to ip 1.2.3.4 (one of your public IP's) on port 80 then forward the information to 192.168.1.230 (for instance, this could be the private address of your web server).
Or
If traffic comes into Port0 to 1.2.3.6 on Port 443 (ssl) then forward information to 192.168.1.120 (for instance, this could be the private address of your exchange box with OWA enabled for this address).
This is VERY basic examples. ASA's also have DMZ zones which adds another layer of protection from the outside. You can use NAT translation to make your private server's private address "appear" to be the public Ip address that is forwarded to the private. many many options.
