I think they are just 20 bit on the front end and they get decimated down for the output so they have 16 bit outputs. It's just that the filtering is done in 20 bit, they throw the last 4 away for you.
On the JB3 AD, I had a thought this weekend. You could maybe slip some insulation foil between the disc and the board to help isolate the analog lines. I don't remember how tight things are in there but it seems like something could fit in there. May be worth a shot but it sounds like you have resigned to an outboard ADC.