Shortly after implementation we started running WHD as an "application" in Chrome - basically so it runs in it's own window with no address bar etc and runs from a separate shortcut- which helps I think to get out of the mindset of it running in a browser.
Anything that would normally open in a new tab or downloads open in your browser but you tend to switch back to the main application window to what you are working on. Seems to work for us but will admit it's a workaround to a limitation, not a solution!