OK Greg, here I go again with a new approach based on your suggestions. Please review it and tell me if it is OK or not.
I use a +2.5 V reference for the ADS1274 ADC. The common-mode input voltage of the ADC is 2.5 V, too.
With a reference voltage of +2.5 V in the ADC, the full scale range of each input is +-2.5 V (or 5 V peak-to-peak).
Since the systems to be measured have a differential range of +- 3.3 V (or 6.6 V peak-to-peak), the gain of the input stage must be 2.5/3.3 = 0.7575...
Using the THS4524 quad fully-differential amplifier, I choose the biasing resistors of each stage to have a ratio of 0.75 (feedback resistor to signal-connecting resistor).
Another thing is that the signals to be measured have a large output impedance; this means that the biasing resistors of the amplifier must not be of the order of 1 kOhm, as in the datasheet, but larger. I have chosen values of 100 kOhm and 75 kOhm, or 200 kOhm and 150 kOhm. Is it safe to use such large resistor values with this part?