The answer to restore your sanity is to configure the router to use NAT (Network Address Translation). That way your servers use private (RFC1918) addresses within your LAN, as do any other devices. The servers need fixed addresses, but everything else can use DHCP (exclude the addresses used for the servers). NAT will also allow all the other devices to communicate to the Internet, which you probably already have configured.
Then the router translates one of the ‘real’ static addresses and translates it to the private address that the server is actually using. For better security, limit the NAT to only the service (TCP port) you need translated, so if it is a web server only nat traffic to TCP port 80. That way you only need one NIC card on any of the servers. Also is the servers are providing access on different ports, say one is a web server and another is a mail server, they can both have the same external IP address, but the NAT translates the specific port to the correct private address, so you save on the number of fixed ‘real’ IP addresses you need.
Even cheap routers should allow you do do this. Look for Address Translation, or port translation, something like that.
Also remember to disable any services on the servers that are not needed, it helps to protect against attacks. And finally, make sure you have a good firewall if you are exposing any server to the Internet (the firewall could also do the NAT if the router can not).