Perhaps Prince Henry could marry a Younger sister of his OTL second wife..
Henry's OTL 2nd wife? he could marry her first, in fact. John's 2nd wife only has 1 younger sister, who is still a decade or so older than Prince Henry.
The marriage to Anne of Bohemia seems rather unusual - but if Richard II did it, who knows. Although, one thing's for sure - John II could just legitimize his illegitimate children and marry the 2 Mortimer daughtersand one son off with them. Or just tell the girls to "get thee to a nunnery" and the guys to religious training (as indeed one of his illegitimate children seems to have been.)