Semi-Presorted post can be acquired pretty easily. Places like Shippo and PirateShip offer it. As long as you put enough money into the postage paid, the post office doesn't really give a shit if it comes out of somewhere weird. There is no requirement that "return address" and "sent from" area are the same so long as they're within the same postal zone.

This is why AMZN packages have a return address in Vegas or similar sometimes.