This will sound like a silly question, but this is all new to me. If I were to remove the nut entirely to what extent would the neck continue to bow away from the strings? I'm not going to snap it am I? If anything I'm releasing tension but there must be a point at which the neck will stop bending as the truss rid ceases to have any effect.
(I'll loosen the strings before loosening the truss rod I imagine. That might actually be the answer)