Can you make a video to just figure out why the temperature probe reading varies so much across your 3 instruments?
I'm fairly sure it would be due to the meter's ability to determine the cold junction temperature and do the math to compensate for it. Google "cold junction compensation for thermocouples". There will be a little math an physics involved.
Nice work on checking out the software! Pretty cool it can extract out all the manual save points. I'm guessing it if you just read the values over the raw COM port text you wouldn't even need to install anything either. Majority of the reason to have an "integrated" resistor network is so that all of their temperature coefficients match very closely, so even if the values drift, their ratios won't. I guess it's not quite needed for 4.5 digit DMM.
Yes, you could issue SCPI commands like "comf" to change functions and "meas" to get the values. I think you are right on the resistor packs. You can add to the that some ADCs don't have individual compensation for the analog channels. Older designs especially. My old Fluke 8050 has a Caddock net in it. Of course, it was fairly high end in it's day.