I've identified the error in my thinking. I was thinking of the pendulum as a classic gravitational system wherein the connection between the center of mass of the pendulum and the pivot is a rigid body. That's not the case in a torsion clock, in that the connection is a spring.

For the rigid-body case, T=2(pi)*sqrt(L/g) where T is the period, L is the length of the pendulum and g is the force of gravity.

For the spring case, T=2(pi)*sqrt(m/k) where T is the period, m is the mass of the pendulum and k is the spring constant. (Red highlight added because this is the point Wayne is making.)

The basic period of a torsion pendulum is set by the mass and spring constant, but fine regulation is set by changing the center of mass of the pendulum relative to the centerline of the torsion spring. This is the effect of conservation of angular momentum (the same phenomenon that causes a skater's speed of rotation to increase as she draws her arms in close to her body). It has nothing to do with the rigid-body period of oscillation.

When we're choosing a new torsion spring, we're playing around with the spring constant k - the only variable in the equation we can adjust unless we change the weight of the pendulum. The calculation of k for a given torsion spring is complicated in that there are a large number of factors that affect it, not the least of which is its overall length.

I have a standard Kundo I bought without a pendulum that's running a Schatz pendulum because that's all I had. I had to choose a different suspension spring relative to what "The Book" says but it runs great and keeps time well. I played with the m/k relationship to get the T necessary.