Is there any way for the Lancasters to not lose power in England without some control measure that would bankrupt the treasury?
c) If things deteriorate such that Henry needs to be deposed, opposition could rally around his cousin rather than York (who wasn't all that well-liked among his aristocratic peers).
Not having Henry VI be literally insane would also help, if you prefer that. Although that obviously requires a 1421 POD (with a different egg being fertilized). Likewise if he had sane brothers (which requires Henry V living slightly longer, something that has wider implications), for more or less the same reasons as Henry having Lancastrian cousins running around.
This would be one for interesting times. If the young Edward has a hint of his father's "melancholia", then the inevitable machinations will increase sevenfold.An interesting alternative would be to kill off Henry VI after his son is born but before the break with York becomes unavoidable. A regency is nasty and dangerous (especially one that's going to last over a decade and have a claimant to the throne as a logical regent), but still probably better than being shackled to Henry VI.