Today, I took a fresh look and discovered solder damage from my probes on the ADC pads. That damage chipped some solder, and it was shorting across pins, I believe. The attached picture is after I picked the bits out, and you can see them lying on the board. My ham-fisted probing isn't compatible with modern solder.
I've cleaned the debris, resoldered the pads, cleaned the board, and started over. However, it is back to the original symptoms, so I'll start again. Given the OLVD indication everywhere, I suspect a short somewhere that's causing power to feed into the AMPs. At least that's the tack I'm going to take. I'm also going to measure reference voltages and document more observations. I'm hoping something will pop out as abnormal.
Thanks.