Make sure and check the rear suspension as Kenneth mentions. Has the steering box been checked out? Maybe one of the springs in the tie rod ends is broken? I drive trucks everyday and have never had a "death wabble". Keep digging and you should figure it out. Save your $$$ for other parts and pass on the steering stabilizer.
When it comes to hot rods and steering stabilizers its a different situation, most of the time its mis matched parts and or different weight bias that are off. A stabilizer shock does help those cars. Other applications are 4 wheel drive trucks that are jacked up and have over size tires can benefit from them.