Problem with LCD and Motor

From the photo, it looks as if those solenoids are held together by 4 screws with hex or Torx heads. It might be worth disassembling one, to see whether there is room to fit a diode inside (although that will probably invalidate the warranty). If space is limited, then depending on the current taken by the solenoid, you may be able to use a smaller diode. You can also get 1N400x diodes in SMD packages.