Using the DAC7311 EVM and an external reference on J2 pin 20 I noticed that the voltage going to the DAC7311 was much lower than the input reference voltage.
The cause of the discrepancy was the R2 which is a 10k ohm resistor and on the output of the OPA353 put in a voltage follower configuation. Active current is around 80µA for the DAC7311 which would equate to a voltage drop of 800mV across R2. Changing that to a 100 ohm caused less of a voltage drop.
I would recommend either connecting directly to TP1 and TP3 for the reference.