Ask the manufacturer for a shipping label. If its under warranty, they likely will pay for it.
If its not under warranty and you have to pay shipping, ask them for a shipping label, since they make dozens of them every day, and that you will pay for it with a credit card.
If that doesn't work, call ALL of your local FFL/pawn shops and ask them what they charge to mail a firearm back to the manufacturer. They can use USPS, and can ship it cheaper than you can via FedEX or USPS. My local guy charges like $10 plus postage, so about $20 to $25 ish to ship a gun.