The Kingdom of Germany did exist, but then Otto the Great conquered Italy and established the Holy Roman Empire instead, which lead to the title of German king losing its meaning. Before proclaiming himself emperor he had been reasonable successful about getting the German nobles under his thumb and defeated the Pagan Magyar/Hungarian at the Battle of Lechfeld, largely ending their raids into central Europe.
However while establishing the HRE was a great achievement, I do not think it did much good for Germany in the long run. The conflicts with the Pope were already flaming up at the end of Otto the Great's life, with the Pope trying to incite rebellion in North Italy.
If you can have Otto I live his life up until after the Battle of Lechfeld but then butterfly away his conquest of Italy then I think in the long run a more centralized Germany is very likely. This way there would be a King in Germany, not an Emperor. He would still have to deal with German and West Slavic nobles, have conflicts with France and Denmark, but most importantly he would not have to endure the headache that was Italy and the Pope that the Holy Roman Emperors had to deal with. He would not have to divide his focus between Germany and Italy, which would benefit him immensely.
If you want to spice it up further, give Italy to the French King somehow, have him proclaim himself Roman Emperor and let France deal with the Italian/Papal headache.