You forgot the most obvious Lancastrian claimant, Edward Stafford, Duke of Buckingham.On the Lancastrian side, you have three possible heirs to Henry VII, none of whom has an excellent claim:
And on the Yorkist, obviously Elizabeth, who would need to be matched to one of these and would most likely not be allowed/able to rule on her own.
- Jasper Tudor, his closest male relative, an adult general and half-brother of the late Henry VI, but entirely lacking in Plantagenet blood: he'd have to marry Elizabeth, claim succession to Henry VII by right of conquest and election by Parliament. Constitutionally, it'd be real messy.
- Charles Beaufort, later known as Charles Somerset, bastard son of the late Duke of Somerset, a male-line Plantagenet. Some vague argument for a secret marriage between his parents could be made, I suppose.
- Edward Plantagenet, Earl of Warwick, on account of his father's Lancastrian dealings, and being a male-line Plantagenet.
I doubt it. Her father and uncle were two of the most hated Englishmen at the time. Plus, there is still the legitimacy of the Beauforts and if they are allowed to inherit the throne. Combine that with other claimants running around and I can’t see Margaret getting the throne.What about Margaret as a temporary measure? A Queen regnant unlikely to produce heirs, but able to stabilize the country and nominate an heir (someone like Lincoln).
Depending on where they are at the time of Henry’s death, I could see Jasper and Oxford playing Kingmaker, installing Edward of Warwick on the throne in hopes he will be a puppet. They might even try to marry him to Elizabeth to beef up his claim. Meanwhile, John de la Pole, if he was made privy to Richard’s plans to name him heir, would likely organise a revolt against the new regime. Lovell and other surviving Ricardians are likely to support him to. So if John, goes for the crown we could see another civil war break out. If not, then the plan to put Warwick on the throne could succeed, though there would obviously be some revolts along the way. Alternatively, Oxford and Jasper could support John and beg for mercy. Personally, I see a civil war happening no matter what happens.