Great idea! I will give this a try! Crazy if something that simple solves the lid issue. Of course I AM trying to make a silk purse out of a sow's ear and I realize that.
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Keep in mind you're not going to make a silk purse from a sow's ear so I'd keep the effort / cost at a minimum.
That being said, I've added screws to tighten up the cedar slats at the top until they just drag when you close the lid. However, this makes the slat corner gaps - which are usually pretty pathetic already - even bigger so now you need a dot of sealant at each one. The bottom can be helped by adding a slab of thin plexiglas like has been posted. You can also rip the felt off (wouldn't do this unless it looks like it's going to peel off easily) and replace it with adhesive back cork gasket material. That will seal the bottom up better than felt but probably not do quite as nice a job as the plexi on the inside. Anything more involved than that, I don't think I'd bother.
The simplest thing to do would be to toss the entire crappy humidor into a cooler or tupperdor.
I wouldn't put cedar on the outside, it would be pointless.
What about putting it inside of a cooler? Lots of folks use cigar boxes to organize their coolerador, this would just be an oversized cigar box :)