Dropdown Options Modal Styling

I have a docked view that I'm using as a page header that contains a dropdown component. For the dropdown options (.ia_dropdown__optionsModal CSS class), I'm trying to apply styles via the stylesheet that only apply to the dropdown in this particular docked view. With other types of components that I want to directly target with CSS rules, I would typically achieve this by putting a domId on the parent view.

The issue I'm running into is that the dropdown options modal doesn't actually nest under the dropdown components parent view in the element hierarchy so anything targeted at the parent view domId will not apply to the options modal for the dropdown. Is there a way to achieve this targeted styling via the stylesheet resource or is my only option at the moment to use the dropdownOptionStyle property on the dropdown component?