Haha I went through this during a beer trade, and you're right USPS is really the best option. Those flat rate priority boxes are great. Got across the country in two days for about $12, which beat USPS and FedEx's $30ish for 7 day shipped.
Best part is you can get the box at the store but then go home and print your label and package it up yourself. You get a discount for paying online. So I was able to go to the post office, have a friendly conversation with the dude, and drop off my sealed package no questions asked.