Considering Catherine Parr was married for her "nursing skills" and Henry liked her because she took care of her invalid husband(s) quietly and without complaint, SFJ is probably correct, although it baffles me how a higher Si with lower Ne wouldn't be more careful in pushing her agenda with a man who had proven himself (and she had the benefit of watching ALL the wives fall) to be psychopathic, unstable, and intolerant of people telling him what to do.
Even Katharine of Aragon was careful in how she dealt with him, and she only had experience, for awhile, with Henry being a minor asshole, rather than one who chopped all his former friends' heads off.
ETA: Cromwell was a highly effective INTJ. His biggest mistake was one of "what's useful" (Te) over "emotional connections" (inability to understand Henry's irrational "but she stinks, and I don't like her" reaction to Anne of Cleves).
I've actually seen ESTJ proposed for Katharine of Aragon, considering she out-maneuvered her husband so skillfully during the divorce and managed to stay one step ahead of his lawyers; she had to represent herself, for the most part, throughout everything, with little advice, and in many ways was indeed, as Anne Boleyn so bluntly put it, "sure to have the upper hand" in any argument with Henry. But... her intense emotions seem to ride closer to the surface than I'd expect from an ESTJ; I can't see an ESTJ writing "woe is me" e-mails to Spain for years on end, nor being incapable of managing her household expenses and letting others handle her affairs as KoA was after Arthur died. Even if you can make an argument that she was young and without experience, I think Te might have stepped in sooner, decisively (she eventually did, and was incredibly efficient at everything she did, though, so... maybe I'm wrong?).
BTW, Cardinal Wolsey was an ESTJ. Brilliant man.
Thomas More, I have more trouble with. One of my INTJ friends say INFP; but he seemed to use Te very well, at least with his job -- he kind of single-highhandedly went in and cleaned up the entire backlog of criminal court cases in his appointment to the office of High Sheriff; he was also an effective Lord Chancellor. His intense focus on the intangible, on higher things, his philosophical letters to Erasmus, his endless satires, etc., suggest Intuitive dominance of some kind -- but he lacks the singular vision and EXTREME forward thinking of Cromwell (Ni), so... I can see shades of INTJ at times (particularly in some of his prophecies about Henry -- he said rather early on that he may consider himself a friend to the king, but if the king might win a foreign castle by giving them Thomas More's head, he'd do it) but... I dunno, could INFP be correct?
Erasmus, though, there's a ENFP for you. Intense, theological, offensive, and thought-provoking all at once; his morality bled through once in awhile but fell beneath "I can turn everything into a joke" -- which is probably why I like Erasmus so much.