After a couple of weeks more experience working with CSS in iAD Producer, I think I have an answer. Any styling that is added using the inspector panel will overwrite anything in the Global.css file even if it is subsequently reset.
I concluded this after discovering the following significant issue with CSS in iAd Producer: any styles on labels applied using the inspector will overwrite anything in Global.css even if, and this key, the inspector-applied styles are deleted afterwards.
Leave a label's inspector properties untouched and assign it a class name. You will then be able to style it's background colour, say, using Global.css. But if you first or subsequently assign a background colour using the inspector panel this will overwrite the Global.css even if you subsequently set the background to None in the inspector panel. I assume this is because it is literally applying a background-color: none
property to some hidden CSS file somewhere in the background.
Why the original question font isn't being applied now makes sense: as all text labels are by default created with Helvetica Neue as a font, applying another font has to be done via the drop down in the inspector panel, not CSS. One workaround for this is achieve by importing custom fonts into the assets panel for this purpose.