Without analyzing the requirements of what you are doing I would ask the following things.

What kind of range of A/D conversion do you need to convert any one given type of thermocouple to the resolution you need?

If you said 16 bits then I would not design with a 24 bit converter but instead with a 16 bit converter. You will realize a more successful project if you dynamically re-configure the converter per thermocouple type, using the lowest number of converter bits possible.

It is not always the best solution to measure the distance from the earth to the sun with a ruler with 0.01 mm resolution.

Second, you mentioned a 1V fake ground. Is it possible, and if so, to subtract this 1V out of the readings through use of a differential type amplifier configuration instead of making the software assume its 1 volt and having software subtract it out. I suspect that you can eliminate at least one calibration constant by doing this. You can never get the 1 volt level as accurate as the resolution of a 24 bit coverter.

Michael Karas