Orochi Iori Yagami:
If I switched to AV Cables would it slove my problem?
No, AV cables prolly won't work, you'll need a RGB cable but I guess your US TV doesn't have RGB/scart ports. Anyway, give it a try just to make sure.
Arakon's suggestion seems the way to, get a cheap old Amiga monitor such as the 1084/1084S (S = stereo), a Philips CM8833 or a Nec MultiSync 3D/4D and a RGB cable for your Genny. You can find these monitors for about $50 to $80, depending on condition and setup, sometimes for less. Yes, they're quite small, but if the tube is still okay, they deliver a very nice and clear picture. Also, they are compatible to both PAL and NTSC, even to odd stuff like PAL-60 or NTSC-50.
Another way would be to buy a signal converter but they are quite expensive.