there would be much cheaper options, most microbreweries, beershops, online beer clubs etc have all cut a good deal with the post office for whole cases of beer for as little as around 12 bucks. So at a guess for a one of from joe blow couldn't be more then 20 bucks for a whole case of beer. don't quote me just yet.
If you have others you know of sending beer such as clubs etc you could all go in together and send a case.
I don't know how to use the system to get the cheapest rate but can find out, there are plenty of brewers on here that would use the system to send cases of beer to individuals almost everyday.