If Edward's advisors are still as influential then I think Jane Grey will be the nominated successor in Edward's "will". Mary, Queen of Scots' claim would depend on who she is married / betrothed to.
If OTL Queen Mary is dead then the other choices would be a Catholic Portuguese infant, an Orthodox Russian infant (or some kind of Personal Union with Russia?) or the intended of the heir to the Catholic King of France. Politically none of these have a strong enough internal power base to combat the supporters of Lady Jane Grey in my opinion but it would open up a multitude of potential external players in an English Succession war