Customizing IE address bar dropdown

I would like to customize the contents of the dropdown that is displayed in IE when text is entered in the address bar (the default implementation displays results from history, favorites, etc.). According to Spy++, the window that contains the dropdown is a DirectUIHWND. Apparently this window class is undocumented and the application is using custom painting to put content in it.

The best idea I've come up with is to hook the events that cause the current window to be displayed and display my own dropdown instead, with my own content. Obviously I'd rather find a cleaner way to customize the contents of the existing window, however, and I'm wondering if anyone has any pointers about how this might be achieved.