Rather than repeat all that, can you try some USB to HDMI adapter like this one? It's only to test if that would work and not the final solution as USB 2.0 may not be up to the task of 1080p playback.
http://www.amazon.com/gp/product/B00BPEV1XK/ for example.
If your Apple has USB 3.0, should work.
Bob

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