When it arrived it was the complete solution to my problem. The adapter doesn't list it on its features, but it does have EDID masking. It caused the Ouya to output 1080p. With that, there was nothing on screen. But I had already installed xposed and the mod collection, So in 640x480 I set 720p from the collection and rebooted. Its working perfectly now, and I've got a cheap game and media station at the foot of my bed.
I bought the HDMI sound adapter from here. It doesn't have any latency I've noticed and doesn't require any power. Probably the cheapest solution to this problem too, I pinched quite a few pennies on this. I came out of this spending maybe $90, as I bought the Ouya from the promo sale that had it at $60.