Alternate 1066 - what kept Sven Estridsen away?

Sweyn II of Denmark claim to the Throne of England comes, via his mother Estrid, from his grandfather Sweyn Forkbeard, who was declared King of all England in 1013.

Sweyn Forkbeard died in 1014 and the Throne of England past to his son Cnute the Great and in turn it past to Harold I Harefoot, son of the union between Cnute and Ælfgifu of Northampton. Harold I didn’t last long and he died 1040. He was succeeded by his half-brother Harthacnut or Cnute III, son of Cnute and Emma of Normandy. Harthacnut also didn’t last long, and he died in 1042 and the Throne allegedly past to Edward the Confessor, who was the half-brother of Harthacnut – his mother was Emma of Normandy, and his father was Æthelred the Unready who had been King of England before Sweyn Forkbeard invaded.
The line of succession became chaotic following the death of Edward the Confessor for there were at least four men who tried to enforce their claim to England. Harold II Godwinson, Edgar Atheling, William Duke of Normandy and Harald Hardrada, King of Norway. Each had claims to varying degrees.

Harold II, Edward’s brother-in-law, claimed that Edward, on his deathbed, promised the throne to him. He enjoyed the support of the Witan

William, Duke of Normandy was a distant cousin of Edward through Edward’s mother Emma. He claims that Edward had promised the throne to him, and that Harold II had sworn his allegiance to William and acknowledge that he was the rightful heir. William enjoyed the support of Emperor Henry IV and the Pope.

Harold Hardrada was a chancer, his claim stemmed from an agreement between Magnus I of Norway and Harthacnut. The agreement stated that whoever died first without an heir the survivor would inherit. The agreement pertained to the Crown of Denmark, but Harold who had tried unsuccessfully to claim Denmark turned his attention to England, which although outside the scope of the deal Harold nonetheless claimed that he was the successor of Harthacnut and tried it take the throne.

Edgar Atheling had the strongest blood-tie to Edward and was the last of the Royal House of Wessex.

Sweyn II inherited Denmark from Magnus and held it despite Harold Hardrada’s attempt to take the Kingdom. When Hardrada was killed Sweyn II looked to England and joined forces with Edgar Atheling, but William paid Sweyn to effectively betray Edgar. Sweyn II tried again in 1074/75 but these failed.

Sweyn took York before returning to Denmark. If Sweyn had not taken the money and done a runner it could be that the alliance may have dislodged William... Edgar probably wouldn't survive.

I'm reading my new book of Sven Estridsen - his problems with Harold Hardrada made him ask the support of the Church which he got along assurance that he were the rightful ruler of Denmark, Norway and claimant to England. Being so reliant upon the Church and William having obtained a Papal Standard for the Conquest of England may this have been the real problem?
I am well aware that Hamburg-Bremen was something of a nuisance to the Papacy because of its wanting to gain supremacy of the Mission in Scandinavia though on the other hand at times it used Papal letters to pressure a King like Sven Estridsen. Thus the two could end up in the Church NOT supporting Sven regarding England but having no problem about his doings in Scandinavia and around the Baltic.