Error deriving temperature from thermocouple amplifier
The circuit looks fine. Unless you have the wrong connector (needs to be matched to the thermocouple)


  I have discovered experimentally that the temperature measurements
  produced by my firmware from reading the ADC the AD8495 is attached to
  are off by a factor of between 20-30% of the "actual" temperature as
  measured by a commercial IR thermometer that I have.


IR thermometers create their own problems (like what material am I looking at? what is the emmissivity?) Not a good way to get an opinion on temperature. Use another thermocouple. Make sure the both thermocouples are thermally tied to the same temperature in the same way. (when the thermocouple is hot, the cable is cool and this can throw things off a bit if the thermocouple doesn't have a good connection to the material with the temperature of interest.

I use a 289 fluke meter. Even then, in my opinion below 10C between thermocouples is decent and below 5C is great.