Updating with a solution:
I was able to do this by creating a json config for my page with some minimum properties that Jambo / the theme seems to expect. These were verticalKey and pageTitle (the key can be anything, since there’s not a real vertical we’re connecting to). It the latest release of the theme I also had to add verticalsToConfig (I just made it an empty object).
In order to prevent the page from causing errors on the other pages I needed to add excludedVerticals: [<my fake vertical key>] to all of the other configs.