So, the datasheet really isn't clear what the input range is.  There are some formulas and stuff for input range and other things, but nothing _really_ makes it clear.  So I'm now using VDDANA/1.48 (~2.2V), with an input gain setting of 1x, and I'm just going to full-scale everything from 0V to 2.2V and call it good.  To this end, I'm going to change R4 in the reference generator to 2.2kOhm, which should give me a 1.0-something center reference.  R15 is also instead of being 1k to make a 1/10 gain ratio, I'm going to use 750 ohms (1/13.3 gain ratio, about).

At the very least I'm producing 4095 data values, so I know things are working.  Mostly.  Because I forgot that I left a power supply connected while powering up the MCU. So I fried one of the output mosfets, whoops.  Good thing it's just a 2n7002....