I disagree with your statement that heating both junctions to 200 or three hundred gives no volts. They do give volts, but they cancel each other out, so there is no current flow. You had the right conclusion, but for the wrong reason.
You might disagree, but a thermocouple's EMF is generated because of the temperature gradient - the difference in temperature from one end to the other. It is not the absolute temperature that generates EMF, it is the difference in temperature.
Measuring the voltage across a thermocouple with a DVM is also a misleading test. The DVM lead to on wire on the thermocouple creates a junction, and the other DVM lead to the other side also creates a thermocouple. So now you are not measuring the thermocouple voltages, but a new voltage from the three junctions. This voltage would be created from the difference between temperatures in the three junctions.
If this were true, then thermocouple thermometry would not be practical. A thermocouple analog input circuit uses conventional electronic materials (copper, brass, nickel plating) as conductors to sense the thermocouple's millivolt output, (optionally) amplify it and feed it to an A/D. So any conventional thermocouple transmitter, controller, handheld meter, or AI card would be subject to the limitation you cite.
However, the thermocouple
Law of Intermediate Metals applies, which says that intermediate junctions (of the same metal composition) do not affect the T/C EMF output if the intermediate junction measurement points are isothermal, that is, at the same temperature.
The issue with measuring a thermocouple's mV output is trying to relate the mV value to the temperature listed in a thermocouple mv/temp table because the cold junction/icepoint compensation is not taken into account.