I've looked into it carefully. I am also suspicious of the Kelvin clips. I have every so often seen a negative value of D (implying negative resistance). I was testing various capacitors including a batch of three Soviet PTFE all of the same value. The capacitors had large silver-plated stub terminals that were quite corroded, so I polished them clean with metal polish. I measured D of -0.00014, -0.00014, and -0.00015. That suggests something solid, not an iffy connection.
I had also wondered about the S/C calibration and on one attempt, I got rather larger correction values than expected, leading me to clean the Kelvin clips. A little dirt was visible on the cleaning paper. After that, the S/C calibration produced more familiar values.
I'm wondering about a piezo-electric effect and mechanical stress because of the fact that leaving a capacitor in the jig overnight and switching the Hioki on immediately gives a stable and sensible value of D, whereas inserting a silvered mica capacitor seems to require 120s or more for stability; the Hioki now has a kitchen timer nearby. Film capacitors do not seem to show this effect nearly as badly as silvered mica, making me wonder about dielectric absorption.
The measurement jig is destined to get an internal RTD so that temperature can be logged, and a couple of white LEDs inside so that I can more easily see what I'm doing. After that, those Kelvin clips may have to go, but I really don't want to have to poke a soldering iron in there every time I want to measure something. One possibility is to make another jig for soldered connections, but it's quite a lot of work...
Meanwhile, I logged a Vernitron silvered mica capacitor for two hours. The drift in capacitance is not due to temperature, perhaps supporting the mechanical stress hypothesis. The D for the Vernitron silvered micas was nowhere near as good as the Soviets, suggesting poor quality control of incoming material. Never thought I'd praise Soviet quality control! Of course, Vernitron couldn't send naughty employees to the gulag for ten years. Lab work is stopping now because weather forecast says it's going to be hot for the next week...