If you're planning on just using a power resistor inserted inline to drop some voltage, that only works if the input current to your monitor is actually constant, which it never is on a monitor (just do a black screen vs. white screen test to see this, let alone startup transients and running the degauss coil). There are some ways to do this using "really stiff" voltage dividers, but the power dissipated in the divider would be insane (we're talking space heater levels) to get the kind of load regulation you desire.
As an example, say your monitor is rated for 1A, but you're displaying a black screen, degauss is off, etc. It may only be drawing half an amp. So if you had a resistor in-line to drop 120V to 100V on the assumption of a 1A draw (a 20 ohm resistor), you'll only be dropping half that, and you'll be applying 110V to the monitor. You can go the other way, too. Usually, the rating is "steady state" and won't include startup inrush. On inrush, some monitors can draw several dozen amps. Suddenly, that resistor is basically dropping you down to almost 0V (and getting REALLY toasty)!
A variac or transformer is the best approach here. Note that if you can get your transformer apart somewhat, you can re-wind them to change the turns ratios and get other output voltages. Getting it apart depends on how the thing is constructed (sometimes it just isn't worth the effort).