George of Hanover's claim to the British throne came from his mother Sophia of Hanover, who was the daughter of Elizabeth Stuart, the famous "Winter Queen" of Bohemia. Looking at Elizabeth's other children, there were several before Sophia, but it seems none of them had surviving issue by 1707. One of her first children was Charles I Louis, Elector Palatine, who also had a son, Charles II. He was a fairly incompetent ruler, and when he died childless the Electorate passed to the Catholic Neuburg branch of the family. In this scenario, let's give Charles II a son. He married in 1671, so if he has a son around 1680, he could be a vigorous 20-something by 1707. How will having an Imperial Elector as King affect British history? It seems the Jacobite rebellions will still take place, but other than that I'm not sure.