I got you now. I didn't realize you wanted me to run it from the HDMI switch box to the overhead projector directly. That's not going to work though as I only have 1 DVI/HDMI cable running from the back of the unit to the overhead projector and the Optoma overhead projector only has 1 HDMI input (plus there's no way I'm going to attempt to fishline that cable up the wall and down the ceiling to the projector.
I could put the PS3 & HD-A3 into the 970 DVI inputs and run the 970 DVI output into HDMI Switch A. Then run the HDMI directly from the DirecTV box to the HDMI Switch B (and use the Video 1 / Coaxial audio as you suggested), that may work. The only thing that sucks is that I have a cheap monoprice HDMI switch that doesn't have auto switching which means I'll have to continually keep getting up to switch sources.
I also didn't realize that the 4th Optical input in the back of the 970 was actually a Optical Output, so I now understand the need to use the coaxial audio input for the DirecTV to connnect all 4 digital audio connections in the back of the unit.
The way I have it hooked up right now is I left the PS3 into the DVD DVI connection and hooked up the HD-A3 into the DVD Component connection. I select DVD and as long as I only turn on one of the units at a time, the 970 appears to be able to select and pass the video signal for the unit that is on. The downside with this method is that I will have to go into the menu to select the correct audio input to get sound to match. I'm going to try to work up a macro on my logitech remote to automatically switch the audio inputs and see if that will work.
Thanks again for your help.