After a few trips to Tap Plastics and the hardware store, I figured out there were two basic choices for how to stick Lego together permanently -- Krazy Glue (or its equivalents) and epoxy. Krazy Glue's benefit was ease of use -- a simple tube applicator. I thought epoxy would be stronger, and I liked the idea that it didn't bond instantly so there was room for mistakes to be corrected. The most important factor, though, was strength, so I devised a simple way to test their comparative strengths. I glued together cantalevers out of 1x2 bricks, and put weight on the end of each one until it broke.
 
 

My garage-based elegant solution included a C-clamp, a bathroom scale and a bucketful of dog food. I clamped the lego to the workbench, hung the bucket off the end, and added dog food to the bucket until the lego snapped. As it turns out, a bucket of dog food weighs about 10 pounds, so I ended up putting a scale in the line and pulling down until final breakage.

Krazy Glue won, holding 18 pounds compared to the 16 pounds that epoxy held. Interestingly, the Krazy Glue held rigid until catastophic failure, while the epoxy slowly bent and finally gave way. For a guitar, the rigidity is crucial. Krazy Glue became my krazy new friend.