TRRS connector with iphone circuit board, how to get mic compatible with PC input (Bose Q25)
Here is an in depth explanation of jack pinouts http://www.cablechick.com.au/blog/understanding-trrs-and-audio-jacks/

Its super late and im glancing at your problem in my seprate search on a different subject that lead me here but based on what i read from your problem and what that websites says it seems like BOSE swapped the pin locations on the TRRS jack to make it hard for people to use it with anything other than a bose product. One thought I had would be to make your own "adapter" by taking a female TRRS jack from some other bose component (if you dont mind partially screwing it up) and wiring that female jack to a regular male TRRS. Hope this helps man  JUST NOTICED I overlooked some info in your post. but im too tired to delet the irrelavent stuff i suggest you take a look at the diagram for an Iphone TRRS on that link i posted i feel like it will answer your problem. let me know how it goes!