We would definitely not recommend trying to drive the buffers using the ADS1278 directly; it needs to be buffered. You are correct in that you do need to be careful of the capacitive loading on the output of op-amps to keep the circuit stable. You may need to employ a small R in series with the capacitor or close the feedback loop around the series R (you can refer to the reference buffer circuit on the EVM for an example).
TINA is a good tool that we have that allows you to simulate the response of the circuit.