I was wondering if I could get a list of the symmetrization methods out there i.e. methods that rigidly transform a set A into it's equimeasure ball $A^{*}$.
Here are some:
a) Steiner Symmetrization
b) Two-point rearrangement
c) Schwarz Symmetrization
d) Continuous symmetrizations (using homotopies)
e)
Of course most of these don't transform $A$ into a ball at once, but can be used to get there in the limit. I would add spherical symmetrization to the list; slicing $A$ by concentric spheres $S_r$, then rearranging each $A\cap S_r$ into a spherical cap (say, centered at North pole) of the same spherical measure. This is a generalization of classical circular symmetrization employed by Pólya and Szegö.
You will find most of these, plus elliptic symmetrization (plus some things that are not quite symmetrization but work like it) in Symmetrization in the geometric theory of functions of a complex variable by Dubinin. It concerns the planar case only, but extensions to higher dimensions can be imagined... or found in Capacities and geometric transformations of subsets in $n$-space by the same author. Also, if you are in Toronto, you should not have to go far to find someone to ask about symmetrization.