Picking the right sensor for a military style alarm
What about ultrasonic sensors? SparkFun carries a variety of sensors, ranging from ~$30-$100, and it looks like some of them have ranges that get close to your 10m requirement. The one issue is angle; you may have to use more than one to cover a 60° swath.

Your concern with radar would apply here too: it will only measure distance (or Δdistance) from the sensor. But to me this is almost a good thing; it detects "presense" instead of motion, so it could not be foiled by moving really slowly like a motion sensor is. You could program your Arduino to do collect say a hundred readings when powered on, and calculate thresholds to trip the alarm based on, say, the difference between the max and min reading (eg. int high_threshold=max+(max-min); int low_threshold=min-(max-min);)

The benefit I see of ultrasonic over PIR is that the readings should be fairly stable through a variety of conditions (lighting, temperature, etc), whereas a PIR will need to compensate for the variation and/or suffer false alarms. And of course the benefit over laser/actual tripwire is ease of setup.

This will probably consume more power than a PIR, but it shouldn't be too much. This sensor claims to draw 3.1mA when powered at 5V, meaning it should last ~160h on a 500mAh 9V battery (regulated to 5v; this doesn't take into account losses from the regulator), but of course the Arduino and radio will cut that a lot shorter.