Currently there are no efficient workflows for working with multiple repositories. I have to open the Repository Browser window, choose the repository I want to work with, find the Repository Browser window, close it, do actions on the selected repository, close it's window then invoke a menu command or press on the Dock icon again to reopen the Browser.

I think this should be avoided if you changed a little bit the way this works. I think you should think only in repository windows instead of the Repository Browser + repository windows. I think Safari is a perfect example: you can open as many windows as you want, they open with a list of bookmarks (in Source Tree: saved repositories), the user selects one of them or adds a new one and uses the same window to manipulate the selected repository. After he or she finishes, closes the window. Much cleaner workflow, and lacks the need of opening and closing the Repository Browser manually.

To be clear: I think you should integrate the Repository Browser's contents into the main (repository) windows, and let the user select some save repo then change the window content to reflect the repo window.