The neck came alongside the body in a packing box. This one would have been hard to get loose as the other body parts are still tight and strong. If the body was falling apart and back separating. I'd have worked the back off with a utility knife and wiggled the neck to loosen it. If the fretboard lets loose of the old body, the neck will usually come free from rocking the neck back and forth. I've got several necks loose this way. Resetting the neck is much easier if the back is off. Then you can get at and clamp the neck block to reset the neck and clean the parts properly.
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Will be watching this. How did you get the neck off?