I am Icelandic and not without knowledge on Icelandic history. The fact is that Iceland with the peculiar system of governance it had in 1066 could never have waged war on any county in Ireland or wherever. Sure we managed a total force of 2300 combatants in the 13th century and we had a naval battle (where the side one that had the good sense to fill their boats up on rocks prior to setting sail). But these were local clashes where farmers could be coaxed into leaving their farms to avenge some slight on the ruling clans honor or for pure power grabbing. A far cry from sending levies on a crusade.
See thats where your wrong. Only takes the right person in the right place and any country has the ability to do things far beyond its current abilities whether the majority of the populace was in agreement at the time. Most great dictators started off in countires in just the right period where the circumstances are just right for a momentous occurrence whether good or bad. Who would have thought a jumped up little Austrian corporal could have led Germany into trying to take over Europe just after it had lost so many millions of its men and been defeated in WW1. Less than 20 years later and its all gearing up again. If you spoke to people in 1919 or 20 would they have thought it a possibility, probably not.
So the right (or wrong) person in Iceland in the 1000s and history could have been very different, all thats needed is the potential, and there was more potential in Iceland than is currently available. A jarl/chief etc could have united Iceland and taken some of Norways islands like the Orkneys Faroes, western isle etc. Not beyond imagination. Even northern parts of Ireland were susceptible in this period of time because of the Gaelic feudal system.
The way I see it the game should be as factually correct as close as possible to make a good game up until you get control, then its history re-written, like its meant to be.