Turns out that some of the I/Os that I was using on the dev board for AD0-AD7 did not go to 3.3V as they should (not sure why.) They only went to ~2.0V and so the AMC1210 did not see them correctly. Plus the lines were very noisy. I switched to other lines and that fixed the issue. I have not yet tried reading current from the sigma-delta, but now I can write and ready back from a register correctly.
There is still a question in my mind regarding the Integrator register. If it is not enabled, do any of the settings in that register do anything?
Thanks.