I did something similar, and it worked out simplest to forward from one router to the other. Then everything is verified from the context of the parent router, and ~p works as expected.

It could be more prominent but the clearest docs for this are under url:

Forwarded routes are also resolved automatically. For example, imagine you
have a forward path to an admin router in your main router:

  defmodule AppWeb.Router do
    ...
    forward "/admin", AppWeb.AdminRouter
  end

  defmodule AppWeb.AdminRouter do
    ...
    get "/users", AppWeb.Admin.UserController
  end

Forwarded paths in your main application router will be verified as usual,
such as ~p"/admin/users".