Check out uBrowser. Trust me.
More importantly, download the source and checkout the bug page. There are only a few remaining show stoppers, but they're tricky. The biggest is the fact that we don't properly handle control inputs in plugins, like Flash. So, think you can fix it? If you do, I'll give you a private island in Second Life, including both the up-front cost and the monthly dues for one year. Note that the solution must work on Windows, Mac, and Linux -- or, if we've fixed it on one or more platforms, on the platforms that are still unsolved. I'll post updates here as we move along. For two other bugs -- creating new windows and feedback dialogs -- I'll reward the intrepid coder behind the solution with the ability to create a new last name within Second Life -- with the expected restrictions that the last name must pass the Community Standards and subject to the approval of the Customer Service Team.
So, go play with uBrowser and help us to help you!