If it's a bolt-on electric, I'd take the neck off and just pack using the clothes as packing material (literally!). I've done this a few times - though I was using a monsterous samsonite hardshell case that could fit a bass neck in diagonally!
For customs...Hmm, make sure it looks used - remove all tags, protective plastics,etc...if stopped you can either : debate that you bought it secondhand or say it was bought new, but you've used it for quite a while. I've not yet been stopped and have brought in 4 acoustic guitars (3 new, one used) over the years.
I have practice breezing through customs - a confident walk and the mindset that "there's nothing to see here" works well
One thing to consider...if it's a 'replica' you might run into some savvy customs agent looking for such things - incredibly unlikely though.