The Battle for England that Never Happened. (Theme Help)

I'm working on a game involving a battle for control of England. I'd like some help enriching the theme and making it more accurate.

The map of England I'm using shows the continent divided into 9 regions roughly corresponding to the Earldoms just prior to the Norman Invasion.

Point #1: This is a somewhat abstract euro/war game spanning the continent involving 2-4 players (Earls?). I know that during this period the King lost much power to the Earls who were often in dispute amongst each other for territory. But from what I understand (please correct me if I'm wrong and cite examples) the conflicts that arose were not normally violent and were more often resolved politically. This doesn't fit my theme.

The military units I have in play (and this part is pretty solidified) are infantry, pikemen, archers, cavalry, catapults, trebuchets and stone keeps.

Point #2: From what I've read the use of archers, cavalry, stone keeps and siege equipment didn't come about until well after the Normans took over. (Before that castles were mostly made of wood and were generally burned down during a siege - not busted open with flying rocks). This also doesn't fit my theme.

I'd like some help resolving these historical discrepancies, or at least explaining them. I'm open to shifting the time period, changing the roles of the players, or even moving the whole thing to a different continent if anyone could think of a different setting that my mechanics would match more closely.

Also, what would everyone think of leaving everything as is and calling this a "what if" scenario, as in "What it the Earls continued to grow in power and the Normans never invaded or were repelled?"