This has been mentioned in the other threads, but maybe everyone hasn't read it. I actually have a Motorola 3400 Dual Tuner HD DVR box from Comcast. I use a $30 2x1 HDMI switcher to go out to my projector from the cable box and it works great.
If anyone has the 6412III with HDMI and isn't having luck with their HDMI switching reciever, I recommend this cheap experiment. Perhaps the 6412 will have the same luck.
I could have gone with the 4x1, but didn't feel like spending the extra cash at the moment, maybe in the future.