"For 20.000v you'll need a 16 bit DAC"
The OP has not specified what type of control yet. Yes, I agree it will need a high order DAC, probably a 24bit if you want to work around DAC non-linearity if he wants digital control. Personally, I would advise againt digital control, digital adds noise into a system and at mV/mA you need to avoid noise at all costs.
"here's a reason why ~$100 and even ~$200 power supplies have only 2 decimal digits."
"0.001v is 0.005% of 20V, which gives you an idea of what tolerances / required thermal stability you'll be working with."
The OP has asked for help in designing/building a PSU to mV/mA - so let try to help him.
It is good in pointing out the issues, how do we over come them?
"when the temperature of the pot will change you'll see a noticable change in the output voltage because of the pot's thermal drift. "
The OP has not said that thermal drift is important. I agree that this need to be considered when working to mV/mA resolution.
So we need to make sure the design includes a high precision V reference with low thermal drift AND that the pots used also have low thermal drift.
(Still cannot believe UK voted out
)