The solution is a simple one: run a development website in parallel, so that all changes can be tested on that first. Updating the primary website would be like flipping a switch. Here’s how I managed this:

1. Set up a new virtual host for the development site.
2. Set up a new database for the development site and populate it with existing records.
3. Update the WordPress configuration file to select a different database based on the current working directory.
4. Set up server authentication for the development website.
5. Write an init script to copy (rsync) all the files from the development site to the primary one. Exclude the authentication files like htpasswd, of course.
6. Set up a dependency on the new script in Apache, so that restarting the service also restarts Apache (this is useful at times).

It’s as simple as that!