I wouldnt worry about it... you have a bunch of people nit-picking the rules. At its dimensions you will more than likely not have a problem. IFyou do, you can u-box it and place it in the overhead or check it. I wouldnt be worried about someone pilfering your huge monitor as much as I would be worried about someone stealing a small pocketable item like an ipod.

If you're really that worried about it, put it in a checked piece of luggage. Most companies who drop ship monitors just slap a label on the box and send it through UPS or the post. They're designed to get jostled around a bit.