How to route outbound traffic to specific domain "XYZ.org" via a specific NIC or public/static IP? [closed]

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http://serverfault.com – Within the next week or so, I'll be setting up an AT&T U-verse modem with 5 usable static public IP addresses. I plan to register a domain name pointing at 1 of the 5 static IPs, and run a website from a single server setup in my home LAN. I'll skip the long winded reason why, but I need to somehow source route outbound traffic (originating from my server) destined for one public domain (i.e. http://www.sample.org) to be from one of the other 4 static IPs only. Basically, I want this public domain to see connections coming from an IP address and not my domain name. If it makes it easier, ()