Justin, I'm using Structure, which I just love---but boy, did I have to do a lot of alternate sidebar files to get the right things to display in the right places.
One thing that might have cut down on this was the ability to designate some widgets as universal, so they displayed on, say, all right sidebars throughout the site. Naturally, I also want to be able to have the flexible sidebar content you've already included in Structure, for categories, single posts, etc. Right now, I'm doing this with includes added directly to the sidebar files, and custom sidebar files for home and certain categories.
I'm not sure this type of control is even possible in WP without users mucking about in the theme files the way I did---but I'm sure if it is, you would know how to implement it.