Shared permalink path for taxonomy, custom posts and pages

I’m building a site where I have a custom post type called “Cities” and have a taxonomy called “States”, and I want to have all pages fall under the path /places/.

So for example, a city Scranton page is rendered at:
/places/pennsylvania/scranton

And a city Las Vegas is rendered at
/places/nevada/las-vegas

I also set up a Page item that serves as a landing page for these, and it renders at
/places/

I’ve been able to make all of these URLs functional, except when I create a Page that is a child of this main page, it is showing up as a 404. For example I created a “Help” Page and made its parent the “/places/” page. This path is a 404:
/places/help/

Any suggestions on what I can do to make this work? I see a workaround on this thread (https://ww.wp.xz.cn/support/topic/shared-permalink-path-for-custom-post-type-custom-taxonomy-and-regular-pages?replies=2) where I could put these sub-pages into a different path, but I would like to avoid doing that.