Remove the monitor and manually degauss it. Keep in mind there is only one way to properly do this. If you do it wrong, it will not help the problem....possibly make it worse. Make sure there is not a speaker with a large magnet in the cabinet. This is *important*.....'specially in a cocktail cabinet where space is cramped. They used those "cheap" alnico slug magnet speakers for a reason....because the alnico slug mag is very focused within the VC gap and doesn't throw much stray magnetism around.
They look like this guy here:
http://thumbs3.ebaystatic.com/m/mbNFIGMZFXO9eLQh7Ebf7QA/140.jpgDon't use car speakers or anything with a large grey "ring" magnet. Those shouldn't be within 3' of any kind of monitor....
If you can find a 6x9 speaker with a neodymium magnet, that *may* work....but I can't say for sure since I've never had to try it. They would look very similar to the alnico version, but I have no idea how much stray field they have.