ccurtis:
Your explanation is a bit confusing, but suffice to say that Thermocouples depend on temperature differences and are highly non-linear/ The tables depend on a having the reference junction in an ice bath and measuring the difference between two thermoucouples.
The connections at the isothermal block are known as half-junctions and you want them to have the same change with temperature, Hence, isothermal.
The compensation circuit may only be valid for a certain range of ambient temperatures (The temperature of the block).
You need:
An isothermal connection and the exact temperature of that junction, called the reference junction.
You need the measured voltage difference.
Using software, you can tailor the parameter that you need.
(1) You need the voltage that would be measured at the 1/2 junction temperature as if the reference is 32 F (from the tables)
(2) You need the voltage difference between the two 1/2 junctions (one at the TC and one at the measuring element)
From those numbers and some polynomials, you can determine temperature.
This
https://www.mccdaq.com/usb-data-acquisition/USB-TEMP-Series.aspx was one of the worst performers for TC measurements. It did fine with RTD's. All it took was a fan blowing on top of the terminals and the output was wrong.