1. Would you check PSRR simulation and measurement under Iload=0mA see any difference?
2. Would you check Vac amplitude when testing PSRR see if Vac too big to harm your OPA already
3. If you have RC filter for VREF externally, you can also test PSRR of VREF first see if as expected
4. If still problems, welcome to post your schematic and simulation results