It's out of left field, but Gloucester could marry Princess Ulrika Eleonora. better known as the sister of Charles XII and his successor upon his untimely death. She married quite late in life, and the two were born only a year apart. With the Wars of the Spanish Succession and the Northern Wars raging, Ulrika would made an attractive candidate as a bride for the prince as she is Protestant and of a suitably royal house.
Another big plus is that Sweden was quite pro-French in the 17th century, the absolutism of the king being bankrolled by French subsidies, much in the same way that Charles II ruled without Parliament for some years by accepting French money, although he never went the full step of quashing parliament in ruling.
In this anti-French atmosphere, he Whigs might see their chance to gain further influence in the Baltic. Russia isnt really recognizing on their radar, who certainly had more connections to the empire and Germany than England. The Whigs could also offer to sweeten the deal by offering subsidies to replace French ones. It'd have interesting effects on the Northern War as Sweden could still lose, yet with Charles XII still living. Ulrika would be a perfect Queen for England. She didn't meddle, was religious, and very charitable. They also share a relative: William of Gloucester's father is her uncle.
It could be interesting if such a match went through and was later regretted because of Charles XII's gaafes. It certainly wouldn't be the first time, such as Charles II with Catherine of Braganza, François Ier with his daughter-in-law Catherine de Médicis when her dowry went unpaid...
I would have the pair marry say in 1705, 1706. when they are between 15-16 for Gloucester and 17-18 for Ulrika. Charles XII at the height of his popularity. And as a butterfly effect talks are resumed for Charles XII to marry Princess Sophia of Denmark (who counts Queen Anne as her amongst her aunts; the duo were also betrothed and it was broken in 1697).
It's from there things could easily go up or down, such as say, Charles XII spent raised from the Riksdag for his sisters dowry being spent on military campaigns; Charles being taken prisoner and appealing to his sister for aid. Especially if William has succeeded his mother, it could create an uproar in Parliament if Ulrika sought to pawn her jewels to secure his release.
There is also that very tricky issue should Charles XII die without any heirs. IOTL, the so-called "Hesse" party secured Ulrike's election, based on her marriage to Frederick of Hesse, and her having served as Regent. IATL, there would be no such party and Ulrike would've never served in such a capacity. Charles XII had a second sister, Hedvig Sophia of Holstein-Gottorp. She was the eldest sister of the three and was actually the heiress presumptive until her death. She lived in Sweden following the death of her husband and headed the so-called Holstein Party to have her son Charles Frederick recognized as heir. In 1708 there was even talk of her remarriage (the OTL George II was a candidate!). It was his capture at a military camp that led to her early death.
Ulrike's marriage to William gives many butterflies. There's no chance of Charles XII suddenly dying (although given his lifestyle and fighting with his troops, I wouldn't rule it out). No marriage to Frederick of Hesse, which was a late marriage in 1715. Ulrike and William have chance issue. And thirdly,should Charles XII never marry, he will certainly pull a Christina and name his nephew by his eldest sister as his heir; she seemed to harbor no ambitions of being queen, but certainly had ambitions for her son.
Mostly importantly, this probably butterflies away rhe Age of Liberty in Sweden, although I could be wrong, which would be huge. If Sweden turns to be pro-English, it may lead the Russians to court the French even more so than OTL, and would definitely have great effects of British domestic policy if Charles XII proves himself ungallant such as, like I said, spending his sister's intended dowry to fight his wars, and even later on Queen Ulrike seeking an increase to her Parliamentary Annuity to pay her brothers ransom to be some juicy 18th century political scandals for the Whigs.