Surely if Harold Godwinson is defeated at the battle of Stamford bridge he won't want to fight william but will instead go for support in the midlands (possibly) and defintly the west country. A prolonged war would make Sveyn see his opportunity and so he will probably invade slightly earlier. Perhaps just to add to confusion Harold Godwinson could guarantee the independance of cornwall in return for help against William. This could just force some sort of treaty since William is nearly bankrupt and the country in a pretty bad way with William controlling the south east and possibly london Harald Hadrada controlling northern England maybe up to the wash, sweyn controlling East Anglia and possibly london and Harold controlling the west country (and possibly the west midlands) minus cornwall. Presumably there would be a few border disputes after a while.
I sort of take it as read that Harold dies at Stamford Bridge
Maybe the Welsh kingdom of Deheubarth would be more likely to help the Cornish especially as I have them in a state of undeclared war with William of Normandy