The fun thing about the TC wiring is it's very specific in resistance..... you may be causing some errors as well, using the switch and LED's.... obviously not a lot of resistance is needed to throw bad readings. Not that I'm certain it would work, but ry deleting the LED's at least, to see if it works without them.... The shield of the TC is meant to be un-grounded normally. When you ground the TC housing it's a shield... when you "ground" the other end (open wires end) you are now making a circuit.... no more shielding (or at least a lesser Shield).
I would recommend a separate PID to read the second TC..... it's relatively inexpensive in the grand scheme of things.