However, it might make Anne's position as queen slightly better. She'll possibly still get a choppy ending if she can't deliver a son, but the pressure is off with regards to the fear that Henry can drop her like a hot potato.
Okay interesting.
Well this was what I was thinking regarding Henry and Anne's children:
Edward, Prince of Wales (b. 1532)
Elizabeth of England (b.1535)
Henry, Duke of York (b.1536)
With two sons and a girl there to help, I think that should make her position somewhat more long lasting?
But the problem of the succession was not solved, due to the low fertility of the Tudor dynasty, as already mentioned other times, caused by a rare blood group and a genetic disorder associated (the study of Banks Whitley and Kramer), inherited from Jacquetta of Luxembourg.
Henry’s blood was a carrier of the rare Kell antigen, a protein that triggers immune responses, while the blood of his sexual partners no, making his wifes poor reproductive matches. The study said that in a first pregnancy, a Kell-positive man and a Kell-negative woman can have together a healthy Kell-positive baby. In subsequent pregnancies, however, the antibodies the mother, produced during the first pregnancy, can cross the placenta and attack a Kell-positive fetus, causing a late-term miscarriage, stillbirth or rapid neonatal death

The survival of the three firstborn children (Henry FitzRoy, Elizabeth and Edward) is consistent with the Kell-positive reproductive pattern. As for Catherine of Aragon, the researchers Banks Whitley and Kramer note that «it is possible that some cases of Kell sensitization affect even the first pregnancy», and Mary may have survived because she inherited the recessive Kell gene from Henry, making her impervious to her mother’s antibodies

Henry’s blood group would have doomed the him (as in OTL) to a lifetime of desperately seeking of a male heir, passing from one woman to another.
A disorder, furthermore, that affects members of this suspected blood group, with physical and psychological deterioration in midlife.
Now, the study of Banks Whitley and Kramer makes it impossible the fanciful hypothesis of a long list of survivors children of Henry or that the stillborns or miscarriages in OTL can survive.
Now, in the present TL, a long marriage between Henry and Anna Boleyn would have made more and more restricted the window of opportunity to Henry VIII to have another heir, simplifying, or complicating, depending on the points of view, the succession: four or five years of marriage, accompanied by reproductive troubles as the marriage with Catherina, would have brought the king up to the physical and psychological deterioration in midlife, and up to his resulting impotence.
It now remains to ask: in front of reproductive troubles also in Anna, Henry had decided to rid of her quickly? Once tasted blood, once committed the first murder and realizing that not would have created too many problems, as in OTL he would not have seen problems to cut the heads of the wives in the desire to have a male heir from the next? Or Anna, always in front of reproductive troubles, had decided to play dirty by using other means (the famous incest with her brother) to get pregnant?
Or by accepting the fact of having only two daughters, Henry VIII would work in order to encourage the best succession with a marriage between Mary and James V of Scotland? (Marriage certainly sterile for the same physical problems that have made sterile Mary in OTL...)
What would be, then, the best marriage union for Elizabeth?
However, just a hint: when you have available the knowledge of the clinical picture of a historical figure, you can not ignore "to make ends meet"...
Good luck
