The chapter entitled "Topological Methods" by R.T. Živaljević, in the Handbook of Discrete and Computational Geometry, CRC Press, Chapter 14, 2004, is a good source.

I believe ham-sandwich cuts play a role in regression depth computations, e.g., in the 2000 paper by Marshall Bern and David Eppstein, "Multivariate Regression Depth."

Since you consider the center-point theorem and the center-traversal theorem as applications of the ham-sandwich theorem, this leads to a different proof of the Lipton-Tarjan small-separator theorem for planar graphs, a connection established by Miller, Teng, Thurston, and Vavasis in "Separators for sphere-packings and nearest neighbor graphs," Journal of the ACM, 1997.