Frank pointed out to me that I had dumbly forgotten to include the voltage reference's noise. The LT1031 has an output noise level of ~125 nV/rHz above 10 Hz or so, and this at least makes the estimate much closer. I had also not included an extra LT1125 stage between the reference and the other stages. I guess I was tired.
The estimate is now within a factor of a few of the measured level, and it has roughly the right shape. Around 1 Hz, it looks like the measured data begin to roll up away from the model, though it's tough to say due to the effect of the AC coupling on the analyzer less than a decade below. If there is indeed extra noise here, Frank thinks it could be due to resistor current noise.
I'll switch one or two out for nicer ones and see if things change.