Where’s there a will theres a way. I would say just hard mod it and drill mounting holes in the plastic and just top mount it. You might need to install spacers on the plate on the bottom if there isn’t enough room for the joystick to move around.
2cm… i dont think a JLF would fit then since they are 34 mm deep, are there any smaller sticks? i heard LS-33 are pretty compact but dont know the measurements.