DVI has RGB pins resevered in the connector so in theory you're adapter cable can just break out the analog and display it.

HMDI does not have any analog output pins so you need some sort of D/A converter and encoder to change the digital back to analog for display.

I'd probably just stick with the component (RGB) connections all the way through the chain for the Direct TV. Taking HDMI 3 ft then converting to analog probably isn't going to give you any performance advantage unless the analog circuitry in you Direct box really sucks. Wire up the component cables to the 950 and let it do the switching. This will tell you if you have a problem with the 950 since the Direct box to projector interface works stand alone.

The problem with the Mac Mini might be resolution related. Does the BenQ support resolutions of 1080p? If it only handles 720p or 1080i and you're giving it 1080p it won't lock on. You didn't say what model you have but I know BenQ makes some lower res models.

Hope this helps.