Does anyone know if there's a way to force Knoppix to stretch my monitor?
Look at the cheatcode information at the following link. : http://www.knoppix.net/wiki/Cheat_Codes
Look for anything that would affect the monitor, especially resolution, like "screen=1280x1024" to set the screen resolution for X. I'm assuming that you want to stretch the displayed "Image" and not the actual monitor.

There is a cheatcode that sometimes works in various Linux distributions, but is not listed for Knoppix. I do not know if it works in knoppix and you could try it in an act of desperation. It is "knoppix noddc". You would probably then have to specify the other display parameters using additional cheatcode items. It will probably require a little experimentation.

You failed to mention if your monitor is an LCD, CRT, or a candle in a cardboard box. If it is an LCD, you need to set the resolution high enough to match the native resolution of the monitor. Setting it lower could cause display irregularities like you described.