You've found a limitation of the css scope feature; it can be combined with dialogs but only at the body level. So you can switch in and out classes on the body, but that wouldn't allow you to have two dialogs each with a different class visible at the same time. But that's not really the design of css scope anyway. It was designed so that one widget uses one theme and a different widget uses a different theme.
Another option is to use the dialogClass option that dialog has, though that will take some custom css and will not apply to the overlay.