A low-tech, non-intrusive approach would be to make a tiny unit, call it a Visual Alarm Unit (VAU), comprising a small microphone, audio amplifier (an opamp would do), rectifier and LED. Then mount the VAU on the unit that produces the noise when the alarm system detects movement on your drive.
You could have a socket on the VAU into which you could plug additional LEDS.
Alternatively, you could build a similar VIU that transmitted a wireless signal when the alarm sounded and then have wireless receivers that turned on LEDs anywhere in the house.
You could get really fancy and inject an audio signal into the HiFi system that feeds your headphones.
Mics, Wireless transmitters/receivers, audio amps are all available on the net at a very low cost. As you are in the US component access will not be a problem.
Just a few suggestions.
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PS: shame about cracking the LCD screen- that is just the sort of thing I would do!