Commentator Bobby Fletcher sent me (via comment) this marvelous site of course material of MIT Political Science course "Technology and Policy". Many great lecture notes for the layman including Game Theory, Space Shuttle, Environment, Risk Assessment and Missile Defense, etc.
The relevant data for Taepodong-2 comes from the first lecture of Missile Defense of the Block 4 Materials, where typical missile trajectory (and other technical informations, which are all publicly available) were provided, illustrated by Titan-II missile of the USA, which is also a liquid-fuel rocket based on similar technology of TPD-2. After all, there are not many varieties in rocket technology, such that given certain size and weight, the property of the rocket is more or less determined. TPD-2's technical parameters may be different from that of Titan-II, but it should be within a factor of 2-3, or at worse that of 3-5. After all, it is the weight of the fuel (the type is already known), and the weight of the rockets (with vs without load).
An analogy would be comparing the gas mileage and time to accelerate to 60 mph for a car with known weight, type of engine, and size of fuel tank.
So here is an illustration of based on Titan-II trajectory.
It can be easily seen here how GS's Vick was able to deduce correctly the range of TPD-2 that Pentagon later disclosed. In fact, anyone who has taken that MIT course (or similar ones) should know that.
All one needs is the magic number 42 second (which is observed by US satellite). After the explosion, it is unlikely the rocket continues to fly since it is still under the attraction of gravity (and the velocity might have been lost due to the explosion). Even if the main chamber is undamaged, it can at best double the range based on inertia (gravity drags down the rocket a lot faster than 42 second because there is now no upward thrust). Vick probably made some adjustment based on the load and weight of fuel, but it turned out the results were almost the same, and only 0.1km different from analysis released later by the Pentagon and Japan's SDF.
Since the missile explodes so quickly after taking off, it is no wonder why Japan, Korea and China all failed to detect the event. In fact, Japan's state-of-the-art Aegis destroyer, Kongo (金剛), did not detect any trace of ballistic missiles with its radar. That Japan later disseminated various false information (it flew 640km) was either a desperate act to cover its embarassment or create excuse to re-arm. Given the simplicity of this calculation, the fact that Japanese SDF's announcement (640km) so obviously contradict US observation (35-42 seconds), and the delayed clarification by US (and finally indirectly released via Japanese SDF), is clearly showing US obliged to Japan's request.
Vick also correctly predicted TPD-2 ground trace (i.e. the shadow it would cast on the earth surface had there be a sun directly over) based on the launch angle (itself very hard to measure due to the short time span after took off). It is no where near Pearl Harbor which Japan alleged. Vick actually believed it is more likely it is a real satellite launch (which makes sense for NK, since it is the same technology anyway, but satellite launch has more peaceful element, as Japan tried it since about 20 years ago). If it would land, Vick said it could be " in the south Pacific relative to South America", as illustrated by the orange lines below, which is far from any path to reach any continental. Perhaps conincidentally, the ground tace passes through Tsugaru Strait, minimizing the possibility of falling onto any land mass, and avoid the Japanese main island Honshu, had the rocket failed in the middle of its trajectory.