I think this might be one of those times where I'm the bat. I sent my 5440B/AF into Fluke to get calibrated and they told me that there seemed to be a problem with the high voltage relays.
"Damn" I thought because getting parts was probably going to be expensive. At the same time I was thinking that I saw a not-working 5440B come up for auction. So I grabbed that just in case I needed a donor unit.
It turns out they were able to just give the relays a clean and my 5440B/AF should be available shortly with a complete manufacturer calibration.
This non-working unit was also missing it's fuse holder (I wonder why that is, my other one was also missing the holder) so I got a replacement, fixed up the filter that was pinning the fan in place and powered the unit up.
After an hour or so I checked the voltages and for 10V I'm seeing:

I might have lucked myself into another 5440B for $65 plus shipping.
I'm so chuffed, I just had to share. I'm going to leave it sitting on the bench for a few more hours (Dr Frank suggested 4 for my other unit) and then I'll run both the 5440B & 3458A through their autocal routines and measure again.
TonyG