The Trek 920, Salsa Fargo, or other adventure touring bikes would be a good choice for Iceland. I rode around the Ring Road using 700x35 slicks. We took some dirt roads but we never took one of the interior routes. I'd recommend squeezing in the largest tires possible if you plan to take an interior route without suspension.

Keeping up with the roadies at home is all about changing your position on the bike to get more aerodynamic. People say X bike is faster than Y bike, but really what they mean is that X bike positions me more aerodynamically than Y bike. The good news is you can make changes to Y bike to make it more like X bike. You'd probably want to lower and possibly change out the handlebars and switch tires to something lighter and narrower. Bike weight isn't nearly as important as your position on the bike.