Except most of Simnel and Warbeck's support in OTL came from Richard III's relatives and allies.
To repeat - William Stanley, the man that betrayed Richard III at Bosworth was executed in 1495 by the (rather ungrateful) Henry VII for refusing to fight Perkin Warbeck because he might be Richard of Shrewsbury. Whether you think Richard murdered the boys or not he can easily people of the time did not know and Richard can easily come up with a credible story which would defuse rumors and point to his numerous other not-dead nieces and nephews as counter-examples.
Why would you accept William Stanley's excuse at face value? The man refused to commit before Bosworth Field in order to make sure that he was on the winning team. As the battle of Stoke Field approached he tried to do the same thing, wait for a clear outcome and then support the winner. Unfortunately for him, Henry VII decided to execute him for a lack of loyalty.
His late brother's children were declared illegitimate, the two young sons of his late brother disappeared, and then he became King Richard III. One could see how Richard's contemporaries might get the feeling he offed his nephews. England had been fighting the War of the Roses for generations at this point, and I don't think that anyone at this time held any illusions about the good intentions of those involved in the game of thrones.
Edward Stafford and Edward of Warwick are children. The first won't be a teenager until 1493, the second till 1488. (And Warwick is attainted, has reasons to like Richard, and will be raised by whoever Richard choses.)
The de la Poles were loyal to Richard during his reign and John is Richard's heir.
The de la Poles were adults, and t
Except the Battle of Bosworth did not end the dynastic civil war. Henry VII faced armed opposition for the next 12 years and the last Yorkist pretender died 16 years after Henry did.
At Bosworth neither Richard nor Henry had heavy support. Numbers are notably less on both sides than in most other battles of the War of the Roses, including the Battle of Stoke Field which took place 2 years after Bosworth. Much of Henry's force was mercenaries. And the Stanleys were rather aggressively neutral until they saw which way the battle was going.
It is correct that the first 2 years of Richard's reign did not see peace, but the same is true of Henry VII and he was able to pass the kingdom on to his son. (There was the Stafford and Lovell rebellion in 1486, the Battle of Stoke Field in 1487, Warbeck/Shrewsbury's landing in Ireland in 1490, in Kent in 1495, attempted invasion from Ireland in 1495, attempted invasion from Scotland in 1496, and the Cornish Rising of 1497. Edmund de la Pole's attempts at recognition from 1501 though his capture in 1506 and execution in 1513.)
Henry VII killed Richard III in 1485, and then John de la Pole in 1487. With their deaths (combined with Henry's marriage to Elizabeth of York) the Yorkist cause was effectively dead. With the death of John de la Pole in 1487 subsquent uprisings didn't represent major threats to Henry's throne. The armed attempts on Henry actually gave him an opportunity to eliminate threats to his regime, for example the execution of Stanley.
What long list of Lancastrian claimants? Henry Tudor had a pretty tenous claim and you have already dismissed the claims of Jasper Tudor and the Earl of Oxford. I suppose there's always Margaret Beaufort
These are the adults, in 1485, in order, who have the blood to become the Lancaster claimants:
Ralph Neville, 3rd Earl of Westmoreland
Edmund Grey, Earl of Kent
William FitzAlan, Ear of Arundel (husband of Joan Neville, father of Thomas FitzAlan) OR Thomas FitzAlan
Thomas Grey, Marquess of Dorset (husband of Cicely Bonville, father of Thomas Grey) or his son Thomas Grey
George Talbot, Earl of Shrewsbury (his descent and through his wife Anne Hastings)
Henry Percy, 3rd Earl of Northumberland
Thomas Stanley, Earl of Derby (through is wife Eleanor and his son George, Lord Strange)
John de Vere, 13th Earl of Oxford (through his wife Margaret Neville and commander at Bosworth)
George, Lord Abergavenny
Richard, Lord Latimer