For troubleshooting, I'm using the Measurement and Automation Explorer test panel.
When I set the AI properties to RSE and connect ch0 (any channel) to AIGND, the test panel reads a steady 1.247V. Similarly, using NRSE and ch0 connected to AISENSE, the test panel still reads 1.247V.
If I connect a voltage to ch0, the test panel reads that voltage + the 1.247V offset.
I'm using the PCI 6025E, so there are no jumpers to set. The board passed the online diagnostics including self-calibration.