We had a good experience 3 years ago with a company called TourIs. They arrange various types of travel, and might be able to provide what you need. For example

http://www.tour.is/tours/private_tours.php

We had a different type of trip than yours - 2 weeks, and we did our own driving - but TourIs seemed quite flexible. They arranged everything for us, and it all went smoothly. YMMV.

Good luck. I hope you have a great trip. We really enjoyed our time there.