Some follow-up information:
I decided to have a go at calibrating my unit's DC voltage range. I used 2.10V and 21.0V sources monitored with a bench meter, and adjusted for best results between the two. The trimmer pot was very finicky, but after exercising it a bit I got reasonable results. The meter seems to drift less than it did before, my theory is the trimmer pot may have been a little shaky from the beginning.
The last digit will never be particularly meaningful in terms of absolute accuracy, but as long as the meter is stable, the LSD can be useful for observing short-term trends. My unit was not that stable at first, but it seems a little better now.
During the DIY calibration exercise, I found that if the meter is in ACV range with auto-ranging on, probing a DC voltage of more than about 10V will cause the meter's auto-ranging algorithm to fail with lots of beeping and flashing.
I decided to check the unit's AC performance a little further, since measuring AC in the presence of a DC offset is not exactly an uncommon scenario in electronics. DC power supply ripple, an audio signal in an amplifier, etc.
My test signal was a 200mV rms sine on top of a 10V DC offset, provided by a function generator. On DCV I got a correct display of 10V. On ACV with auto-ranging, I got the crazy display. With manual ranging, I eventually got a correct reading of 0.2V after a long settling time. On the ACmV range, I got unstable readings in the area of 25 mV. It would only produce the correct value of 200mV if I reduced the DC offset to less than 2V.