Well, tried disconnecting the center channel. I have mixed feelings about it.
In my opinion:
Pro: got rid of most of the echo-ey nasal sounding midrange I was hearing. This seems to be a byproduct of these frequencies bouncing off of the glass.
Con: seemed to hurt the soundstaging, moved the sound lower and more into the doors (to be expected). Tonal balance might have been slightly better with it connected.
So I'm split on it. As of now, I left it reconnected, and I'm going to continue to look for other solutions. Adding a resistor to reduce the center volume or attempting some type of passive equalization might work. We'll see, I'll report back if I find something that seems to help.