Turns out the issue was with permissions on the server/host side, got my hosting service to take care of it.
In case it’s relevant to anyone in the future, they said the problem was: “This issue was being caused by incorrect permissions on the wp-content directory. The permissions were 777, but due to PHP being ran as a CGI module (suPHP), the permissions had to be changed to 755.” Something must have happened where they got mixed up when we moved our site.
