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The G-Tech clearly is capable of outputting a display signal, or the above solution with the active DVI adapter wouldn't work.
And since that's the case, I can't see a reason an HDMI adapter wouldn't work if a DVI one does.

That said, I understand your reluctance to go the HDMI route when you know DVI works...

So the DVI route will work with a VGA adapter on the end
and in theory the HDMI adapter route should work

so now I just have to choose between the two... hmm...
 
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