That defineately seems to be a degauss issue. Any CRT type monitor should have a built in degauss coil, whether it is automatic or if you have to push a button. I didn't see anything in the manual that talked about a menu or button to do it, so I would assume it should be automatic. If the case were open you could physically look for the coil around the tube to verify it has one.
Manual -
http://www.dotronix.com/pdf/01054dsvusermanualp.pdfAs far as nearby speakers.... it is their earth magnet that causes most problems. Not sure if you mean they are "shielded" cable wise or what, but make sure there aren't any
physically too close to the CRT itself.
Since the problem kinda shifts and such when you move the monitor, that is a sure sign that it is not degaussing itself. Doing it by hand with a coil or magnet just takes practice.
But I would think it should have it built in......these were made for a video walls.....I can't see someone climbing up and down a ladder or something to degauss every dang one of these every time they are set up.