If you do manage to get UPS, USPS, or FedEx to take it by trying to trick them, it won't be insured. And last time I tried to get FedEx to ship a monitor it was almost freight prices for a 26" anyway. :/
Yeah, as DZ said your only real option is mount it in a wooden box and then crate that. And then freight it. STI, find a friend already making the trip, you can try uShip but you never know what you're getting exactly.
You can also try reaching out on KLOV and see if anyone is making that trip, they have a section dedicated to transportation.