I suspect it depends on Henry's health too. If he suffers his illness/mental collapse in 1453, then things open up for York.
While Richard of York was the heir, he wasn't comfortable in that seat even before the birth of Edward of Westminster. After all, he'd already gathered troops and had an abortive uprising in 1452 at Dartford, IIRC. This uprising was because he was worried that Somerset was going to replace him in the line of succession. Well, that added to the fact that you can't march against the king in the 15th century. It's always his evil advisers that you object too.