I think the headset that you use must support the "Audio Source" service.
When I paired this POS Moto H805 I had sitting in my desk with the curve, it only gave me the "Handsfree" and "Headset" services. I cannot select it while playing any music, and I assume thats why.
I could be wrong, and hopefully someone with a stereo headset can confirm, but I have a feeling that's the problem.
I heard the MotoROKR S9 works, but its headphone style like you said you dont like (I agree, BTW)
Hope this helps.