I'd prefer it be an APT-X, but anything small with good battery life will do.
Why? Well, for a DIY project where I'll be using something like what you see in the pic below, to listen to my phone and make calls.
Have you found a solution for this? I have been looking for some time for a similar DIY project. I have found one product from overseas and one in the US. The product overseas is about $270 with shipping and because it is overseas they won't accept returns. The one in the US has a PTT (Push to Talk) button that I would have to try and get around it.
I also found a device that allow you to either transmit or receive but that only gives you a simplex transmission from a headset. You can either talk to the person or listen to them, not both. I have a MultiPoint headset but that requires which device you want to be paired with.
If you already found something, I would love to hear about it.