I know this is a bit old but thought I'd offer my experience.
We did a moderate deployment of several hundred phones in my company over the course of 2017. Almost all 6930 with a limited set of users on the 6940.
We are having excellent luck with Plantronics CS500 series headsets using the APS-11 EHS cables to connect them. Edit: We did have to configure the phone to DHSG=Enabled.
The 6940s are an exception to that, since Mitel didn't include EHS on them. Those phones use Plantronics Savi headsets via USB in our environment and they mostly work, but clicking the headset without the phone ringing won't draw dial tone. The phone stays on-hook. Clicking the headset with a ringing call answers it, and dialing the phone with headset configured as the default path clicks it on so it's at least functional for them.
At the time, apparently there wasn't much documented information about what was supposed to work (per our vendor) so we went through some trial and error to get to this configuration.
Hopefully that's helpful to someone.
- Heath