The Foundry security primitives for resource visibility (as opposed to data visibility) are largely aligned at the resource level rather than within a given resource. (The one exception I know of that's relevant is within the Object View configuration, where you can set visibility on different Tabs).
An approach also depends on if the resource visibility is a matter of permissions (i.e. should a user outside a given group not see a given page - again separate from the permission to see any data within that page) or one of convenience (i.e. all users can see all the data and all the interfaces, but each given group should simply start in a separate place.
In the former case, (i.e. security) I think it'd be best to make a separate Workshop app for each team and then maybe wrap them all into a Carbon workspace. The resource visibility, configured as the actual resource permissions in Compass, should determine if it appears in the Carbon workspace for the user.
If it's just for convenience, you could build all the pages in a single Workshop app, then make a separate Carbon workspace for each team and set a parameter to determine the default page, as you mentioned.