So... when you bypassed the Integras, you also bypassed the HDMI Switcher. Could this be an EDID problem?
I guess maybe I should add a little more....the cable box outputs run into a Binary HDMI switcher. The outputs run over Cat5 to receivers at the TV's/theater projector. The Integras are being used for audio only. The switcher outputs also have HDMI outs. For the theater, that output also sends HDMI into the Integra.
Looks like you're saying more than one cable box but only one switch....
You've not said how each switcher is connected to each Integra. Do the switchers have dual HDMI outputs, one going to the display and the other to the Integra? Or do the switchers break the audio out of the HDMI and give you an optical audio signal? Or digital coax audio?
Could you go back to the beginning and describe this?