I know that this is not what you are looking for, but I believe it solves the same problem. I too have a fairly large screen and try to make use of it as optimally as possible.
I hate tabbing between code or design tabs and try to avoid that as much as possible.
VS has a feature that permits the user to create Horizontal or Vertical Tab groups and ever since I have started using it, I have found it very helpful. These options are present in the context menu by right clicking the tab or in the VS Window Menu (Menus are seen only if the tab groups feature is not active).
I have created a screenshot with Vertical Tab Groups created as shown below. In this example, I have a overview of both the designer and the code view at the same time.

We can use tab groups whenever there is a dependency such as comparing code, redesigning a module, etc. I know it takes a little time to get used to this feature but try it out and see :)