[ZippySLC]

So, actually what I did was create a new template:

AdminCP > Styles & Templates > Style Manager, and in the dropdown for your style, select "Add New Template."

Name your template whatever you'd like, and paste the code in my first post into the text box. Hit save.

Now, you want to edit the template that the widget that draws that menu uses to use your new custom template.

AdminCP > VBulletinCMS > Widgets and configure the widget for the menu (it will say Section Navigation - JS Advanced). In the popup box you'll change the name of the template to the name that you gave your new custom template.