So, I set up a staging WordPress Pi server, and then set up a second virtual host for the production Pi server (it already had another domain on it). The latter worked fine with php but refuses to play ball with WordPress.
Gah. I think I'll swap out the two, and add a second virtual host to the one that plays ball with WordPress, then reinstall Debian on the old prod one as Staging.
Even then, the Staging to Prod process looks like it might be a bit dodgy.