You're right that the acceleration is not uniform -- as you move closer to the center of the earth, acceleration decreases linearly. This is similar to harmonic oscillation, e.g. a mass hanging from a spring.
I just found a great paper/article backing up the 42-minute claim. (Click the PDF link.)
Turns out you can work the problem the same way by imagining a frictionless plane tangent to the earth's surface onto which you place a mass. Regardless of how far from the actual tangential point on the plane that you place the mass, it will take 42 minutes to make half an oscillation.
Sometimes I miss doing physics.
