There is also the question of what the Staffords would be doing in this scenario?
And there is also the question of Henry VI's Tudor half brothers, although they are likely to young to play any significant role?
Well Humphrey Stafford is married to Salisbury’s sister, so I imagine he’ll side with the Nevilles and therefore York. As to Owen Tudor (and it’s just him, since his sons are still minors as of the PoD), I’d assume he’d be loyal to Humphrey at least. (Then again, he’s married to a Valois...)
That's a really good question about Exeter. I've just looked up and Exter didn't get his Duchy Back until 1443/44 which is after Henry VI has died in this scenario meaning I'm not even sure he is even going to get his Duchy back reduing his influence.
Alternatively, if Exeter feels he is being cheated of his inheritance, he’s be even more likely to throw in his lot with Somerset, adding, if nothing else, more legitimacy to the Beaufort cause; by contrast, if Humphrey or York buy off Exeter’s loyalty by restoring his dukedom, his lack of support certainly won’t help Somerset’s image.
Another wildcard is Henry Beauchamp Duke of Warwick. He was great friends with Henry VI in OTL as well as being the premier non-royal duke of the realm. He may have significant influence over the succession after Henry's death but considering there is no evidence that he was good friends with the Beauforts and Humphrey is Henry's uncle I reckon he wouldn't go against Humphrey. As he dies in OTL in 1446 a year before Humphrey dies he won't be able to impact the succession after Humphrey's death as Humphrey died a year later unless he lives longer in TTL.
Then there is also the fact when Henry Beauchamp dies, Somerset challenged Richard Neville to the inheritance of Henry Beauchamps estates. This will likely further incite Somerset to war or at least consider it as Richard Neville (Wariwck) is obviously firmly in York's Camp.
It sounds like Somerset, if nothing else, will have a huge chip on his shoulder; on the one hand, he may have little support in England to do anything about it, but on the other, the ongoing war in France with possessions in Normandy and Gascony, and the option of agreeing to
non-aggression with the Valois (so that the French focus their energies elsewhere), mean that he has more opportunities to create mischief.