Just an idea I had: if the future Queen Anne had died before her coronation (let's say she has a complication during her last pregnancy in 1698 and dies during childbirth) would William III remarry in order to secure the succession? And who could be his choice? Or he didn't have any intention of remarrying at all, and Sophia of Hanover becomes Queen?
Of course, there are other interesting consequences here. Probably his accident with the mole is butterflied, so we also would have a longer reign for William. How would it affect British politics and the War of the Spanish Succession?