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In otl the execution of Charles I was a huge factor in creating anger amongst Royalists.
Suppose he had died in some other way. Illness or by some hot head or on the battle field.
Charles II was a rather smart operator.
Suppose he had gone to Putney and said he was prepared to agree to be Monarch with a Parliament elected by manhood suffrage. Suppose he proposed a generalise Religious toleration.
I suspect he could have got a Parliament elected very happy to go along with his wishes.