Before you give up on your current monitor, there's a few things to try:
*Check the locations of speakers in the cabinet and nearby stuff. Speakers have magnets...big magnets.
*Re-orient/re-locate the cabinet and try using the integrated degauss again. Sometimes there's just a particularly bad magenetic field in the area either due to surrounding "stuff" or even just the Earth's magnetic field.
*Use a dedicated degaussing tool. These can be had for about $10-15 on ebay or at local auctions. These are much stronger than the integrated degauss, but if the problem is a local magnetic pheonomenon, this won't fix it.
It's entirely possible that, if the problem is caused by some location specific phenomenon, the same problem will appear with a TV.
All that said, yes "standard resolution" is compatible with SDTV video timings, but the input formats are not the same. Arcades use RGB video with a dedicated sync line while TVs in the USA use NTSC composite or s-video or YPbPr component with sync on Y.