Nice chips/breakout boards. I'm still looking for easy to use bipolar ADC to measure +-10V range. Too bad these ones are unipolar.
May I suggest the use of a custom-made ADC driver chip from Analog Devices for this purpose? The 8275 will not only take that bipolar input and reduce the output to 0-4VDC, it'll also create a nice signal centered around 2VDC, perfect for differential ADCs with unipolar inputs.
There's a DIY pre-amp circuit shown on this short youtube. Maybe it will help?https://www.youtube.com/watch?v=aOJuCYgmPPE
You could go for a G=1.5 circuit
Anything else I forgot?
Now I can't say for sure that it is working perfectly...