Instrumentation and difference amplifiers typically lack the precision to work directly with a thermocouple
Huh? That's exactly the sort of application they are designed for, small signals, low bandwidth, good CMRR required... INA128 at gain=100 has typical gain error of 0.05%, offset voltage 50µV...
The AD8230 is an auto-zeroing instrumentation amp has typ 0.01% gain error and max 10µV offset...
Parts like the INA128 and AD8230 are exceptions and not typical, and they still do not meet the performance of the example circuit. At a gain of 100, the LTC2057 has a typical error of 0.00032%, so more than an order of magnitude better.
The Fluke 80TK thermocouple amplifier design gets by with a single TLC271, but has to operate with a very low supply current. I have an ongoing project to replace the TLC271 with an OPA187 low power chopper stabilized part to see if it makes any improvement.
Moreover, the differential input seems very logical for my sensitive ADC converter. Also, does it make sense for me to use an instrumentation amplifier with a lower Vos output and use an auto zero fully differential amplifier on its output? (my output should be differential) At the same time, what is the maximum offset so that I can make a sensitive analog signal conditioner at laboratory level? Of course, cold junction compensation will be made. But how much offset is acceptable at the analog level? Cost is not important. My goal is to achieve as much perfection as possible.
The noise and signal levels for thermocouple measurement do not require anything special on the ADC side. The differential connection to the thermocouple may be preferred in high noise environments, like if the thermocouple was very remote, however most thermocouple applications use a single ended configuration. Noise at the output of the amplifier is going to be great enough that nothing special is required on the ADC side.
Low input offset drift is required for the thermocouple amplifier depending on the operating temperature range of the cold junction compensation, which is typically rather limited in an indoor application. For example with a common type-K thermocouple, the voltage coefficient is 40 uV/C, so a change in input offset voltage of 40 microvolts would be required for a 1C error, and with something like the not so good TLC271 (1uV/C) in the Fluke 80TK thermocouple amplifier, this would mean a 40C change in temperature of the amplifier and cold junction compensation which would be exceptional. Note that 1 uV/C is actually pretty good for a CMOS operational amplifier. Bipolar precision parts can be 0.1uV/C, and chopper stabilized parts may be 0.05uV/C or better, but at this point other considerations become more important.
The input offset voltage is calibrated out with a single point calibration of the thermocouple, so is not a concern, although if the offset was low enough and the cold junction compensation was accurate enough, no calibration would be required.
Modern delta-sigma ADCs are good enough to directly digitize a thermocouple output. No amplifier is required and they make temperature measurement ASICs for exactly this.