You might be able to ship it, packed as above, with Greyhound bus lines. They do take those kinds of things for about half the price another carrier charges. Can you get to a Greyhound terminal on both ends of your trip?
I would not take it on a plane if it were mine unless it can go under a seat. Even so, Bonnie Hunters Featherweight could go under the seat in front of her but someone in that seat had his stuff there and the stewardess did not enforce her right to use the space. The stewardess insisted she check it and the airline broke it and her computer. I don't know which airline it was. I wouldn't trust United, though.