Remove an IP address from server config
Having searched quite a bit and come up empty I decided to just go ahead and remove the registry keys for the IP address I wanted to delete from the configuration.

Steps:


Backup the registry key HKLM\SOFTWARE\Microsoft\Microsoft SQL Server\
Stop SQL services
Go to HKLM\SOFTWARE\Microsoft\Microsoft SQL Server\MSSQL10_50.[Instance Name]\MSSQLServer\SuperSocketNetLib\Tcp\ (must do this for each SQL instances on the server)
Find the IP# key that contains the IpAddress value of the address you want to remove where # is a number from 1 to the number of IP addresses SQL found on your machine during install
Delete the IP# key found in step 4
If the number in the keyname is not the last one, rename the remaining IP# keys to be sequential starting with 1.
Restart SQL Services


After doing this the old IP address was no longer available in SQL Server Configuration Manager and SQL Server no longer tried to listen on that IP address.  There were no longer any "Listening on [old address]" entries in the SQL Log and netstat -an showed no listeners as well.