John de Vere, Earl of Oxford, is Constable of the Tower, which iirc means he has the country's reserves of gunpowder under his control. Any way to guess whom he would favour?
He had no children of his own, and his title passed to his nephew, born 1499, when he died in 1513. Were he to pull a Dudley almost fifty years early, he could maneuvere his nephew into a marriage with Mary and back them for the crown over the rival groups backing Margaret or the Courtenays.
I could see the Courtenays falling into line on the promise that they were to follow Mary and her issue in the line of succession, and Mary would need a Regent, which would probably be Catherine of York and the Earl of Devon (equally could be Anne of York and the Howard's, but Anne had no children) for six years - but the Earl of Devon, like Anne of York, died in 1511.
Let's say the Regency falls to Anne and the Howard's in 1509, but Anne dies in 1511, meaning the Regency passes to Catherine whose husband dies in 1511 - Would a female Regent, not even a Queen Regnant, in her own right even be accepted?
At which point, you've got the Courtenay claim through Catherine, and the De Vere marriage plan due to control of the tower.
Mary marries John De Vere's nephew, and puts the Courtenays (her aunt and cousins) into a senior position at court, eventually making it known that her cousin, Catherine's son, is her heir unless one is born of her body.