Being that the box is hard to find and valuable to a certain degree, I'd take it to a cabinet shop. They could route a place for the lip to maximize your cigar space and prevent squishing your smokes. I think a better place for the lip is on the bottom half of the box. While you're at it, have them cut a small place for your humidifying device and hygrometer in the lid. A decorative latch would finish it off nicely. I don't think this work would cost much. There's not a whole lot of work or materials, just a need for proper power equipment. You might even be able to find a local high school woodshop to do it for free! Do you have other cigar boxes you could donate to the class? The teacher could do yours for an example, and the kids could work on the old donated cigar boxes. You never know.