May be cliche - ehh, but anyways:
Harold beats Harald. Harald escapes in defeat and ignominy, never to be seen from again (ooo, ahh, much spooky, such mystery)
Harold beats William. William escapes in defeat and ignominy, and resettles the bulk of the Normans in Sicily. In penance for that loss the Normans crusaded and conquered North Africa from Cyrene to Tunis.
Harold triumphs in victory and glory, and continues to grow England's
economy. England's happy-go-lucky ways forge the British Isles Gemot, an ever tightening political confederacy backed by a weird protestant/orthodox Anglo-Celtic Church (trust me, this is totally legit). Ship building advances in England for defense, and to facilitate trade in the Baltic and Mediterranean Seas. Finally, Anglocelt fishermen sailing in advanced caravels find a new world west of the Grand Banks in AD1300. The vast land, Hanunah
(Turtle Island, OTL North America), is sparsely populated by friendly communities of Algonquians and Catawba, who are eager to trade with the new comers.
Some decades later Anglocelt sailors exploring the great southern peninsula
(OTL Florida) of Hanunah encounter longships (oh no, who could have seen this coming?!?!). Contact is soon made with the Mabilla Althing. The Mabilla are a league of developed
city-states spread throughout the southeast of Hanunah, who used longships to maintain a trading network across the Caribbean Sea, and even southwest across Zipacna
(Demon Earthquake Crocodile, Central American Isthmus) to the mountain kingdoms in Abyala
(Land of Vital Blood, South America). It is a literate culture that prized industry, hygiene, and education. The Mabilla’s origin was a synthesis of Mississippians with Scandinavian refugees who had fled the Plague of Vinland
(Vinland is the original Scandinavian settlement around the modern day Canadian Maritime Provinces).
Anglocelt explorers brought to Britain codices and new food crops. The codices, written in Mabillan
futhark, concerned subjects such as astronomy, mathematics, medicine, and history. New food crops spurred on population growth in the British Isles, and settlement of Hanunah provided an outlet for the growing Anglocelt people.
Now the nice happy-go lucky Anglocelts brought a certain plant back with them that makes them really happy-go-lucky (oh snap, am I going there? yes I’m doing it!). This gets added to the braziers in the Angloceltic Rite. Angloceltic missionaries had been hard at work in Eastern Europe, and have close ties to Greek Orthodoxy. Happy-go-lucky plant spreads to Byzantines, then stumbled upon by Turks who are now more hungry than hangry. Slowly but surely a Happy-Go-Lucky Planet emerges (Life goal: peace in Middle East – accomplished! you’re welcome, someone had to do it).
6/14/2017 EDIT – Words in blue added, or respelled. Don't post at 3AM kids. PuffyClouds