It would be good for you to log a ticket with support. Reading your description, am I right to say that you would like to remove the "domain" from the "Machine-specific settings" entirely and have it re-synchronized? If so, there maybe a SQL script that support could furnish you.
My mistake Leonard, I thought this was the support portal.
Yes, that is correct. I have several domain names listed under that area (Machine Specific Settings), and one of them has been entered incorrectly under site details.
The script would be very handy, thank you!