@Sebastian_Berlin-WMSE The most straightforward way to set this up would be to have the Wikispeech server(s) limited to localhost access only. You can then use an Apache proxy (or similar) on top of the main server, to allow remote access, and have Apache (or whatever webserver you are using) handle the access control.
It could be set up as a user login, or it could limit access from certain IP addresses only, and there are other ways to do it as well. This setup wouldn't require any changes in the Wikispeech server, it's just about setting it up in the right environment on the server. And it would only require use of standard tools/methods.

This is how we (STTS) would normally set up similar services on our own web server.