Do you have or can you get a reliable precision power supply like an SMU or something and then carefully check it with a scope for output ripple, noise and stability? And then do the same thing as you were doing with the Kenwood model? You could also use the calibrator, but given the issues here you might want to bring in something else.
If you connect one of the malfunctioning meters to a well-vetted PSU, or your Wavetek calibrator and then select the same set of voltages that I tried--0.1 to 4.9V by 100mV steps, then 5V to 50V in 1V steps--then you would have a more complete idea of what might be going on. I'd also do the same with the 34401A (presuming it has not been recalibrated in your lab) just to verify whatever you are using. You also might want to switch the 34401A to AC at each step just to see if there is any ripple.
When you say you have found 6 out of 40 meters to have this issue, do you mean you've tested all 40 and 6 of them behave like this? If so, do those 6 have any common history or use? I would definitely stop trying to recalibrate anything until you figure this out. I'm pretty sure there is no widespread issue with the 187/189 series of meters, but yours could have been damaged by some unusual use or something else in their history. Gross errors like that are pretty weird.
I didn't ask before--what equipment do you have available?