Can't she be betrothed to Amadeus VII, so that there is a possibility of a Savoy France?
Even if the "Richard II" girl was bethroed to Amadeus VII, I think the Savoyard claim would have less chances compared to the English Kings (meaning John of Gaunt/John II of England and his chidlren here) or the Valois.
Plus there had already been one try made by someone who had a claim which can be argued to have more legitimacy than the English Kings or the Valois : Charles II the Bad, King of Navarra.
Charles II of Navarra was the son of Joan of Navarra, daughter of Louis X of France. Proclamation of Salic Law had forbidden Joan to claim the French throne, leading to the reigns of her Uncles Philip V and Charles IV and then to the HYW after the death of the two without male heirs.
Charles II was claiming the French crown as grandson of Louis X, considering his Uncles and the Valois as usurpers. He did several manipulations to weaken both Plantagenêts and Valois so that he could try his luck at taking the French throne. The result? Charles V of France vainquished him and completely isolated him politically.
Domenic said:
John's claim to Castile was through his second wife, and Henry was the son of his first, so he would have had no basis for a personal claim.
True. He could still try to claim it for his wife and the children he had from her, but that doesn't seem necessary given the OTL result.
He had two children from Constance of Castille : a son named John who died young and a daughter named Catherine, who later married Henry III of Castille, the latter being the son of John of Gaunt's rival, John I of Castille (or John of Trastamara).
John of Gaunt could still try to claim Castille for his young son John if the latter were to survive infancy, but the arrangement he had OTL wasn't so bad as his daughter married the next King of Castille.
Plus, I think a John of Gaunt who would have become John II of England would probably have focused on France rather than Castille. The Hundread Years' War still rages on at that point : the English do not really need another front in the southern Gascony with Castille.