It's a 24-inch monitor, and is too big for carry on.
Renting is not an option, as I live in two locations and this is a "permanent" addition to my Budapest office. Cost was the main incentive, being less than half the price in the U.S. compared to sources in Hungary.
Customs is not an issue, as this is personal property, for personal use.
The water bottle suggestion sounds interesting, but I don't have any handy. The tap water where I live is about as good as it gets, and so no need for bottled water.
Played handball today with a friend who it turns out transports an LED monitor as checked baggage on flights to the East Coast, and says he's had no problems using just the original shipping box.
Let's roll the dice!