I considered thst Maria FitzHerbert (or the Countess of Jersey) might queen it fora bit, however, what I can't understand is that the Lords would've even CONSIDERED the thing had it had no long term goal in sight. I suppose they believed thst if the royal marriage was dissolved the king would remarry to produce heirs, but as we know that didn't happen. However, if it WAS just a whim of Georgie, I can't see how Parliament would've just played along. Even if the monarch had more power than it did with Victoria, it's not like George was an absolute monarch (or even that he had as much power as the monarch had had in Tudor or Stuart times)
Under British law, a queen who has committed adultery with a subject is guilty of treason (see Isabelle de France, Anne Boleyn and Kitty Howard). HOWEVER, AIUI from how a former poster explained it, she can't be guilty of treason if she commits adultery with an alien (Pergami wasn't a British citizen AFAIK) so Karoline was TECHNICALLY innocent (even if she had).