> Certifying labs would not be too pleased to hear those arguments.
> Repeatability of specifications in a production line would be a nightmare, as each instrument would have to be treated "unique"

That's the problem (and the solution). You hardly ever see devices of this kind precision.
V. asks for 0.00012% precision. Finding parts of such precision repeatablity is practically impossible. The only way to get such results out of the standard (best available but far from what you'd like) parts is to treat each of the elements as unique. You get a resistor of 1K +-2% and you have the 2% precision. But measure the resistance of this resistor, and you're down to 0.5%. Attach a thermal sensor and measure the resistance in function of temperature and you can use this 2% resistor where you need to know 0.01% deviation from known resistance. Create precise R(I,U,dI,dU,humidity,pressure,light,temp,delta temp,and some more) table, stuff your ultra-precise device with sensors that measure its own conditions and you may just get the precision you require. And you can get these results in two ways - either computationally, by simulating quantum processes in the $0.50 resistor on $1bln computers, or by experimental means, simply exposing the resistor to range of conditions and measuring them. And if you're not happy with either of such approaches, seek 0.00012 % precision resistor manufacturer...