Stephen,
I found what was wrong with my theme. It wasn't using the following code in functions.php, which I found in some previous support posts:
'before_widget' => '<div id="%1$s" class="widget %2$s">',
My parent theme doesn't use the above code when registering widgets. However, I'm using a child theme, and I thought I had properly filtered the function to register the widgets properly (but it obviously wasn't working). My mistake!
Thanks so much for your help, and for the awesome plugin. Have a great new year
Jake