Are there stronger claimants to the British throne than the Windsors?

Answer 1

Not by any reasonable criterion, no. The Act of Settlement 1701 explicitly added Electress Sophia of Hanover (granddaughter of James I) and those of her descendants who were neither Roman Catholic nor had married a Roman Catholic to the line of succession, following William III and Mary II jointly (the current monarchs), either of them individually if one died before the other, their descendants, Mary's sister Anne and her descendants, and any children of William III if he remarried after Mary's death.

Mary died before William, and William and Mary had no children, so on William's death the Crown passed to Anne. None of her children survived her, and since William had not remarried there were no other descendants of James II who were in line for the throne.

That made George I, son of Sophia, King upon the death of Anne (Sophia herself had died a couple of months earlier).

The founder of the House of Windsor, George V, was the legitimate descendant (ultimately, there were a lot of intervening generations) of George I through Victoria I, and in fact "Windsor" was simply a renaming of "Saxe-Coburg and Gotha" (Victoria's husband Albert's house). So it's hard to see how anyone else could have a stronger claim on the throne.

It could, potentially, be argued that the children of Edward VIII have a stronger claim than Elizabeth II, the current monarch, does. However, he didn't have any, and if he had they wouldn't have been eligible anyway, since Edward abdicated in order to marry an American commoner and divorcee, making Elizabeth's father "Bertie" (George VI) king.