Could you direct me where I could change the type label in the search results? For instance, instead of “Portfolio Item” I would like the label to be “Customer Story.”
Unfortunately the results page layout and contents are not affected by the plugin (they can’t be). This is controlled by the theme. I suggest looking at the theme settings – some modern themes may allow you to edit details about the search archive.
If no luck, you can still ask the theme author, it is very likely he can suggest a tiny custom code or a modification for the results page via a child template.