Here's an even more radical idea, although it works better for growlers and bomber bottles.
1. Wrap your beer (bottle/six pack/whatever) in a sealed plastic bag.
2. Line your shipping box with trash bag, so that the trash bag completely lines the inside of the box and is open at the top.
3. Spray in a layer of expanding spray foam insulation into the bottom of the box and let it dry.
4. Put the sealed beer container on top of the dried spray foam.
5. Spray the rest of the foam over and around the sealed beer container.
6. Close up the trash bag and then close the box. Let the foam dry.
7. Take the trash bag/foam/beer out of the box.
8. Use a knife to cut through the foam, slicing it in half so that you can get at the beer.
9. Replace the plastic bag around the beer container and the trash bag inside the container (just in case, to prevent leaks should UPS or FedEx drop an anvil on your box. . . ). Put everything back together in your own custom-made spray foam packaging.
10. Seal the package and ship.