Thank you for contacting us in the forums! Although we haven't tested the Apple HD15 Dongle, I do know with the HDMI converter and Apple TV, you can use the Airplay option to mirror the Slingplayer to the projector. With the Airplay option, if you have the Slingplayer mode set to SQ you will only get audio. It must be set to HQ or AUTO to receive both audio and video. If you have any further questions feel free to contact us. I have provided our contact information below:
Hope this helps!
The Sling Moderation Team