Have you tried it with two TCs connected to your Arduino but both TC isolated from each other, so that they don't share a common ground? It does sound like a ground noise issue. Is there any conductivity between the Arduino's ground and those of the TC? I had to make sure my Arduino's ground isn't connected to the engine/chassis.
My setup is similar, but I route all TC wires to a central box in the engine compartment. An Arduino there is collecting the readings and sending them over to a second Arduino in the cabin. This is on an experimental aircraft.
You haven't said whether your readings are jumpy, or stable but incorrect. Also, is your engine off, or on during your tests? Have you tried to unhook the battery? Basically remove all possible sources of ground noise, then add one by one back in to find the culprit. Maybe you're getting noise into the power supply line of your breakout boards? I'm running all shielded wires, after battling RF noise coming from the ignition system.