Hi Mike,

The BA SAP ECC NA has no relation with the several Platform apps in my opinion. The Platform apps have their own BA's I should suggest.

The red marked ASs depends on the SAP ECC NA Prod AS. Tickets can be assigned to the team supporting the single production instance using Technical service offerings with the same Assignment group  and related them to the Prod instance and the Application instances.
Business Services and Business Service Offerings can 'determine' the different instances as in most of the cases the performance towards the users is different for Prod and Non-Prod instances.

Probably I do not correctly recall from your mail what you exactly mean. Let me know!

Cheers,

Ed