I'm a bit less convinced that a victory by Harold at Hastings would have made little difference though Widimir. William was in a very vulnerable strategic position. He was effectively bottled up on the Pevensey Peninsula, with stretched supply lines and little chance of re-inforcement from over the Channel. If Harold had been able to hold out at Hastings he would have won himself time for reinforcement from the rest of the kingdom, since the Northern earls were already on their way south. Willliam, on the other hand, would have had an army reduced in strength and would still be contained.

A Saxon victory at Hastings would probably not have been the end of William, but once Harold was re-inforced William would have been faced with a choice of facing an enemy greatly outnumbering his own (and consisting of many fresh troops) or beating a rapid retreat over the Channel. Either way, Harold would have won.

And the story of the arrow in the eye didn't appear until later BTW. The contemporary accounts make it clear that he was cut down by horsemen, not felled by an archer.
Cheers,

Thiu