After some digging around and experimenting, I familiarized myself with a few part file fields for the module that handles stock fairing creation. This plugin allows you to tweak a handful of those fields in the VAB via the right-click menu, without having to muck around in the actual part files. These fields were also made persistent so they will stay with your saved vessel and behave as expected after unfocusing and refocusing a vessel.

The fields I chose to make tweakable are the ones I both fully understood (through testing) and felt were the most useful for fairing customization. They include:

Divisions - How many vertical slices the fairing is divided into. ('nArcs' in the part files) [Depricated - tweak now included in stock]
Max Height - The maximum height for each section when building the fairing. ('xSectionHeightMax' in the part files)
Edge Smooth - Roundness between edges of sections. ('edgeWarp' in the part files)