I have written an elementary button JScript that performs web searches from within DOpus. It can use any number of search engines, which are easily configured into the script, and allows searching with one of those engines or with all of them at once. It also allows a choice from multiple browsers, which can also be configured into the script. This script may address some of the questions in the thread above.
It's not very elaborate, but because it is a script rather than DOpus code, I have posted it in the scripts forum instead of here. I hope it's useful to others.