Sorry. I didn't catch the model for the processor but the EDID emulator I linked is probably still something you should consider. It can store and pass on the HDMI EDID information from one device [in your case the Onkyo I think] to another [your video processor]. Somewhere in the chain this...
From an audio perspective I agree with Wayne. For video things can get a little tricky with HDMI handshaking. In order for this process to work properly both the sending [output] and receiving [input] devices need to "see" each other in the signal path. If one of the devices has a delayed...
You didn't list the model number of the companion video processor but clearly that's where the problem lies. If you remove it from the chain and connect the Oppo directly to the projector things should work fine. The video processor appears to use a DVI-HDMI converter to pass along it's...