Henry VIII believed himself to be a loyal and faithful Catholic to his dying day. He was just Pope of England instead of some guy in a country far, far away. The first act of succession (which required the oath as to Elizabeth's right to bypass Mary for the throne) has been repealed by the second act of succession which tossed both H8's daughters out of the succession, with Parliament allowing the King to name his own successor in his will.
It wasn't until Edward VI's reign that the Protestant factor (Edward Seymour & company) took over, brainwashed/educated the king and made Catholicism odious to the crown. (That's how Jane Grey got into the line.)
When in 1540 does Henry kick it? He wed Anne of Cleves in January (I believe) and annulled it months later. He wed Catherine Howard in late July that year (all I remember is it was the same day Cromwell was executed). Personally, I think the Earl of Surrey, her cousin (son of Duke of Norfolk) may just engineer a posthumous son or daughter for Henry if the marriage to Catherine has already occurred. If it's before the annulment, will Anne of Cleves be smart enough or find enough allies to pull off the same?
There are so many possibilities and it depends on the nerve of the nobles involved. Surrey had the nerve, his father has the power, and if Suffolk agrees no Scottish king, they might just pull it off. I would love to see you do the TL.