Address ParametersBase mutation concerns in !37651

This commit follows up on !37651 (merged), in which some members of the ParametersBase class were made mutable to facilitate a unification with the PatternTrackParameters class. Concerns were raised by @christos about the mutability of these data members. To address these concerns we revert the mutability changes. The subclass hierarchy is preserved, although not in a particularly elegant fashion for now.