^I am using a Sapphire HD6950 2GB Flex and use HDMI 1.4a cable ( included in box ) to connect HDMI (from video card ) to HDMI to my 3D TV. It works for me but I am not clear what you mean at 1080p 60Hz? For me it works at 1920x1080 at certain fps ( i forgot but can find out if needed ).
So what is your video card? If it is compliant to HDMI 1.4a then it will support 3D. As I mentioned, mine is working with this set-up.
Why do you look for an HDMI adaptor, doesn't your video card have HDMI port?