Thank you. The aperture time was the culprit. (Again, I was confused by the PXIe-4154, which does not support 'configure_aperture_time'. (It says 'DriverError: -1074135023: IVI: (Hex 0xBFFA0011) Function or method not supported'.)
If I set the aperture time to a reasonable number on the PXIe-4144, it now runs sequences of >>10,000 values (with ~ 1 ms time steps) in the expected time and reads them out in about 3 us per value. I'm happy!