Someone may have a better idea, but if the void isn't large, make some black or the same color of your box sawdust. Pack it in the void and put a drop or two of Super Glue or something like that on the sawdust. It usually hides my screw ups. I guess I should add... do this after your neck is installed.
How 'bout after the neck is installed, just surround where it meets the box with wood trim, covering the bad cuts?
I use black silicone sealer to fill voids on things that are made to fit in a acoustic guitar and the cigar box is flat. Try to keep bead uniform, but you can't so let it sit about 10 minutes and then wet your finger with spit (that is with a "P") and smooth out. In this application I let it dry too long and used a dry finger to smooth. 10 minutes and wet finger works better.
Duct tape !!!!
(I need emoticons!!!!) :-)
Make a patch from the scrap you cut off. Super glue it back on, then carefully re-cut and/or slowly file it to the right size. Check the fit with the neck often as you go, so you don't overshoot again.
Since the box is black, if there are any raw wood edges showing, you can match color with a bit of black marker or black acrylic paint.
Probably nobody will notice it unless you point it out to them.
I like the collar tips a lot! If the over cuts aren't too bad, you could run a thick piece of string around the seams and glue it in place (I'd use Elmer's glue incase you ever wanted to go back into the guitar). It'd be like binding and you could make the color obvious (so it looks like you did it on purpose) or to match the box color.
if you colour the insides of the wood black with a felt tip pen, you will probably not even notice the wobbles. you can also shape a piece of wood to cover the gaps. Wood filler painted black will also do the job.
When I cut a box i cut down to 1+1/2 mm away from the desired size then use a metal square shaped guard to file the shape i need (usually checking with a small off cut of neck size wood regularly) by hand with a normal file.
cut down some popsicle sticks and paint them black to cover the gaps, like shoe base moulding, also called quarter-round moulding, the stuff covers the gaps between the hardwood/vinly floor and the baseboard in your kitchen, or like door frame moulding that covers the gap between the wall and the door jams.