Your old CRT TV will not support resolutions higher than 720x576 or 640x480 (depends on where the TV was manufactured). Forcing 720p video on it will not increase the video quality, and will only introduce artifacts. These artifacts aren't caused by your computer, but by the TV which is unable to recognize the signal properly. Remember, old TVs do not send response signal, which means the computer has no way to control what is drawn there, and in the result, it means that the video will display the signal how it understands it.
It is not a CRT, it is an HDTV rear projection, and there are no artifacts, its an overscan issue (possibly caused by the converter). The TV does not have any settings to adjust the overscan or any auto adjust features.