From what I remember during my trip around Iceland in 2008, there were maybe three spots that were unpaved along Rte 1. All three were in the southeast and east. I used 700c 35 Vittoria Randonneurs, which were fine. The unpaved parts were well maintained with occasional spots of washboard. You could probably run 28s without any problems unless you got the inkling to go inland.
Since I know from other threads that you like packing light, I just want to encourage you to consider using a 4 season tent instead of your tarptent if you decide to go. I have a tarptent and love it, but it would never survive the winds in Iceland. Use something low to the ground with lots of guy lines. It doesn't need to be freestanding because most of the camp sites have a thick enough layer of sod to keep your stakes in firmly.
Iceland is a beautiful place for cycling. Yes, you'll get your share of nasty headwinds and sideswipers and spells of rain, but the landscape is fascinating.