Ok, I need to elaborate a little more:

The LCD is in a partial metal enclosure that snaps shut, which in turn sets into the frame I mentioned. Further troubleshooting has led me to see that simply squeezing the top and left edges of that enclosure with my fingers kills the touchscreen response. Applying such pressure to the right and bottom sections has no apparent effect.

So my next step is to remove the LCD from its partial enclosure. YIKES. I really wish at this point I had found a simpler workaround...

EDIT: ok, the more I look at this the more convinced I am that this is a defective touchscreen. I completely removed the thing from its thin metal enclosure (not an easy task) and squeezing the core component on the left side induces the response failure. At this point there is nothing else for it to contact but itself.

Somehow I have to figure a way to minimize the pressure on the final assembly. Might have to tamper with the faceplate a bit... anyway, bottom line is you guys shouldn't see this, and I'm even more sure that it's not related to the right-side sensitivity issue.

On a related note, I now know EXACTLY what's causing the LED shadowing, and I am vindicated in suggesting that an improved diffuser (there actually isn't one at all) would fix this completely.

EDIT 2: purposefully deflecting the frame a small amount took the necessary pressure off, and the unit now works with the faceplate attached. Yay! One more salvaged device.