removeStyleName ...

Is there a way to remove all the style names that may have been applied?

As compared to removing any style that was applied (which means I have to track what styles are applied)

Something that removes anything/everything I may have applied to a component?

Component.getStyleName() will give you all custom defined style names so just use

Component.removeStyleName(Component.getStyleName());

to remove all user added styles.

Even simpler, you can use Component.setStyleName(null) or Component.setStyleName(""). These too remove only user styles, not those set by the framework.