The Perdew-Zunger self-interaction correction (PZ-SIC) removes unphysical electron self-interaction from calculations employing standard density functional approximations. Doing so improves many computed properties, bringing them into better agreement with experimental observations or with results from high-level quantum chemistry calculations. However, while PZ-SIC generally corrects in the right direction relative to the corresponding reference values, in many cases, it over-corrects. For this reason, scaled-down versions of PZ-SIC have been proposed and investigated. These approaches have mostly employed exterior scaling in which SIC correction terms are scaled in the same way at every point in space. Recently, a new local, or interior, scaling SIC method was proposed on non-empirical grounds to restore a property of the exact, but unknown, density functional that is broken in PZ-SIC. In this approach, the scaling at each point depends on the character of the charge density at that point. However, the local scaling can be done in various ways while still restoring the behavior of the exact functional. In this work, we compare and contrast the performance of various interior scaling approaches for addressing over-corrections of calculated molecular dipole moments and atomic polarizabilities and properties that reflect the nature of the electronic charge density.