GSM Shield interferences

Hey guys,

my project is an automatic temperature controller which sends a SMS if a specific error occurs (Temperature out of tolerance, thermocouple is not connected...). So I have an Arduino Uno with the GSM shield and EEPROM to save the things on, connected over I2C to an Arduino Due with a touchscreen and the thermocouple amplifier MAX31855. The Due is placed on top of the gsm shield. I already milled a case for it, everything fits fine and I can't change it anymore, but I have a really serious problem now. Always when the GSM shield starts sending things, like the initialization at the beginning or sending an sms, everything goes nuts. Transmissions over SPI (Like the thermoamp) are broken, I receive completely nonsense values. Same goes for the rotary encoder. Normally it doesn't affect the rotary encoder since it's pretty rare that the interferences are exactly as the gray code, but the temperature goes completely wild. I already tried shielded cables as SPI wires, it didn't help. I tried to use capacitors (100nF), but they didn't help either. I would've never thought that the radio affects the components so extremely... It's not possible to have an external antenna. Btw., I interconnected the two power supply jacks of the arduinos and just use one power supply for both (But up to 2A, so should be enough). Could this cause any problem? How can I solve this? I don't have much possibilities since it's already done. Anyone may have tips?

Here a picture from one side (Antenna and MAX31855 are on the other side, but cant disassemble it atm):