WI - Otto I lives another Decade, dies in 987/988

Its not just Otto I who dies 973 its also his Commander Duke Herman Billung of Saxony. Which possibly makes for Harold Bluetooth to annex Nordalbingia and get defeated by Otto II 974.
With the longuity of Otto I to 988/9 (that is actually 16-17 years almost two decades) that might prevent Harold from doing such; if considering Billung the real architect of Germans military he may go anyway. I haven't done my homework on Otto - Billung; You may.

The prehistory to Harolds go at Nordalbingia seems to be that following his acession/election to the Danish throne ca. 960 he is baptized (Catholic) 962 and in that year Widukind of Saxony writes is asked by Count Wichmann nephew of Herman Billung to help him make East Holstein independent of Saxony. Wichmann is defeated 967 and Harold then turns his attention to Norway though he also 968 serve to fortify Dannevirke - the border wall to the south. As Widukind knew of Wichmanns asking the Danish King so may others.
Harold then may avoid the defeat by Otto II 974 though he still may see conflict with his son - and he won't lose Norway going independent rather there may be other fighting over Norway.

When Denmark got rid of paying the German King/Emperor tax is unclear; Henry the Fowler had demanded and gotten tax from Gnupa King of Denmark by his defeat 934. Subsequently the following Danish Kings did pay tax - Gorm did and perhaps Harold did. Harold may have renounced tax 973 or Sven Forkbeard did so following his reconquest of Hedeby 983.
Thing is ITTL the Danish King may still pay the Emperor such by Sven's acession to the throne whenever that may be. Though ITTL that may be later than OTL say around 990. Though if the Slavs still revolt 983 the Danish may stop paying tax then if they of course still support their Slav allies.

Now if Sven Forkbeard do conquer England and ITTL don't die shortly following wouldn't this make for some renewed interest in the North at the German court?
As long as the Danish Kingdom pay tax the Germans have their back free in the North and may go as you say on France and Italy rebuilding the Charlemagne Empire - but even Charlemagne didn't conquer Denmark!

Then should Sven decide once England is conquered to renounce paying the Emperor tax what will said Emperor do? Occupy Jutland of course. Charlemagne did so but he didn't get into the Danish isles as he didn't have a Navy to do so; I don't really see the situation much change here. Also the Danish King will have much greater resources with Denmark including Scania, Norway and England as well as alliances with the Slavic tribes/kingdoms on the Baltic making him able to do hit and run raids all over the Imperial coast.
The Ottonians will still have the internal problems with their Dukes and externals like the Saracens in Italy/southern France. Even if they avert the unlucky deaths of the Emperors leaving the magnates room they will still have to rely on the Church to supply a lot of their troops as OTL and will then at the end of the day face the Pope in a kind of investiture strife with other rulers among which the King of Denmark - Norway - perhaps England.
At times even Bishops would enter a magnate uprising in Germany and when defeat loomed not be adverse to taking sactuary in "Pagan" Denmark. Sven Forkbeard BTW was Christian just letting in British Church clergy to counter the Bishop of Cologne who had supremacy of mission in the North NOT Hamburg though Adam wrote so and his writing survived clouding the picture. Prior the Bishop of Rheims had the supremacy of mission in the North with Bishop Ebo 833 fleeing his seat for safety in Denmark during a rebellion.

Just a few musings on the situation in the North!

I think Otto I would have some trouble in bringing a Navy from the Med to the Baltic; it would be possible of course but things would have evolved and it would be sometime later than 974. Harold would still be paying tax so no obvious reason to have a go. With Sven Forkbeard conquest of England around 1000 his son Otto II would have some reason to do so. Still he would have to move his ships through waters infested with longships. Then wait for the German Army having conquered Jutland before moving on the Danish Isles. Of course given luck and determination things may carry through though I don't see it as inevitable and the close the German fleets moves to Denmark it will encounter counterattacks from Danish - Norwegians and English ships. Also there is few ports on the westcoast of Jutland so you basically have to go either north round the Skagen - if they control Jutland the Limfjord is a possible or take the route up the English coast across the North Sea to southern Norway and down the Swedish westcoast. With limited experience of the waters and winds as well as reefs and opposition i don't really see it happening - but its a possible.

Guess this second TL would be regarding Henry the Fowler surviving 936? Hmm, not much to change to the basics. Denmark will be attendin its own affairs with killing off defeated King Gnupa and his son King Sigtryg and then Thyre/Thorvi becomes ruling Queen and have to find somebody suitable to wed to establish the new dynasty like Gorm.

There is this tale of the German Emperor though probably should be King Henry the Fowler intend on marrying Thorvi and she being married continously postponing any talks and fortifying Dannevirke untill she would be able to turn the German proposal down.
Thing is - Gorm arrives out of nowhere (England a possible) and marries Thorvi establishing the Jelling Dynasty.
Then there is also the part of Dannevirke named Thyraborg (Thyra's fortress) which is know to have been in use during Medieval time BUT the German museum of Dannevirke write that there are remains of wooden buildings at the site preceding the Medieval one which may lend credit to Thorvi's fortifying the place. No archeological dig have been done at that site.
Thyre is the one ruling Denmark.

So given circumstances and letting Denmark off paying tax it might be a way to go however the King would still need be elected at the Things around Denmark - North and South Jutland, somewhere in Fyn, Sjælland and Scania and those guys might not be willing to elect a foreigner. Though would the Germans allow a ruling Queen married to a German even a bastard (and William only born 929 so would only be 7 in 934; Thorvi can't marry a child and pretend him to become a great commander and ruler) to be let off tax and stuff? I think not.
The Danes knew Charlemagne hadn't been able to cross Lillebaelt to Fyn so way a German conquest and then Henry would have to go to Lechfeld.. or wherever to defeat the Hungarians.

Not even a snowballs chance in Hell!

Rest of Europe - hmm that would require some reading of mine and sorry but I'm into something other at the mo.

But hey put the squeeze on Count Arnulf I who OTL married Adele of Vermandois 934 to instead marry Thorvi. Flanders being an old ally and possession of Viking rulers and a man of suitale age, Nordic name, and who was willing to take on almost everybody like Normans!!!

Look to Tancred de Hauteville and let William ask Danish Jarl Ulf on his crusader expedition to liberate Galicia, Spain from the infidel to recruit Tancred's sons to go to Iberia instead of Apulia citing the old tradition of Viking Bjorn Ironside battling the Bluemen (Africans) there.
Jarl Ulf set out just a year prior to the Hauteville's first group going to Apulia so its a possible. Jarl Ulf was of the Royal line and ruling in the Limfjord area of North Jutland which was quite a wealthy area. He would be able to travel in style which should seem impressive to the warlike sons of a minor Norman noble.

That would certainly be interesting!

I'll give it a look