Latest prototype is in, and it works great! (Well, there’s always some issue - hence the little wires hacked on near the BNC inputs in the picture!)
One new feature is switchable "super high gain mode", for when your signals are smaller than +-300 mV. There’s some limitations, such as 10k input impedance, and bandwidth is reduced to ~2 MHz in this mode (gain bandwidth product is a killer!). But now you can see signals down to +-3 mV full scale. That’s 20 uV per bit!
Here's a 1 mV 100 kHz square wave. Not bad!