Hello kqed,
Thanks for following up with us!
The section that you would like to customize is actually controlled by your theme when widget areas are registered. If you look where sidebars are registered within your theme, you’ll see that within the “register_sidebar()” function there are two options, “before_widget” & “after_widget” that control what wraps the widget. This is where you can control the class for widgets.
If you need more granular control on a widget by widget basis, you can check out this plugin to see if it helps to get what you’re looking for. I hope this helps.
Thanks!