Encountered Infinite Redirect When Changing Domain Name

My multisite network is running without any problems since I first installed it weeks ago. Today I need to change the domain name to a new one we’ve acquired. I figured all I would need to do is change the server_name directive in my Nginx configuration file, along with any other references in the wp-config.php file.

After restarting, and attempting to go to the new domain, I am experiencing an endless redirect loop.

After some R&D (research & debugging), I’ve learned the database still has the original domain name in various tables. Makes sense, but I doubt the resolution is a simple find and replace of all the values. Though I’ll likely try it once I have it backed up properly.

How do I safely change my domain name without the endless redirect? How can I resolve it? What would you do?

Note: I did not want to use a domain mapping plugin. I greatly prefer having the new domain set as if it were used when I first installed it.

Thanks.