BUMP!
As I create the same pattern as Mr Mackay here I have the same issue. I can set up my App Proxy to work perfect, as /tools or /apps or /a or /community. But as soon as the merchant changes from one to the other, all the JS in the theme no longer points as the right address.
Either you allow the merchant to change URL and allow that change to propagate through a Liquid parameter (if possible), or you send an alert to the App via a webhook so it can re-inject new script code that works with the change.
Leaving the current App Proxy in this state degrades the use case possibilities severely for any App Proxy installed in a general App.