Just posting an update for anyone else who has this model (or is considering one). Never could get the HDMI incompatibility issue sorted out. Industry professionals I spoke with, after listening to my troubleshooting path, remained as mystified as I am. The solution that I came up with works perfectly (although the "why" of the problem is still frustrating); I ran an optical audio cable from the Sharp BD to the HK AVR. The HK lets the user choose between different input paths, so for the BD, HDMI does video and the optical cable handles audio.
With all that solved and out of the way, my long-term impression of this machine is less than favorable. It has crashed on me a few times, stuck at "BYE", requiring a hard power disconnect to reboot the machine. Start-up time is slow, laser servo is loudish, and the "media center" aspect of it is almost worthless as the list of compatible file formats and file systems is rudimentary (my high quality video rips on an EXT4 format drive are inaccessible). Except for the fact that I picked this machine up for pocket change (and got a highest bid of $55 on ebay, even NIB), I would be very dissatisfied. As it sits, it's a functional basic BD in the living room... at that basic task, it will do unto something better comes along.
Speaking of better, my older NAD T557 is still remarkably better than this Sharp BD-AMS20U. The NAD starts a disc quickly and quietly, never crashes, never gives any compatibility issues, and excels at the one thing that most BD players fail at - it ejects a disc almost immediately. That most BD players have to consult with some internal permission system, cycle through a few thousand program cycles, get the disc to slow down, and then finally, painfully, open the tray is something that has always peeved me. The NAD just spits it right out, no muss, no fuss. You get what you pay for.