Title says it all. What if King Oliver I ascended to the Throne?
No no no no no no no. NO.
1) Cromwell is a Republican at heart. He believes (in theory) in democratic rule (provided you are landed of course). He never wanted to be King. This is not in his nature.
2) Even if the DID want to, this would IMMEDIATELY spark a new Civil War. A lot of the best Generals in the New Model Army were Republicans. Infact a petition was made to Cromwell threatening to overthrow him if he DID accept the crown. Cromwell is popular, but not popular enough to keep a huge chunk of the New Model Army moving against him.
The only way you'd be able to get Cromwell to agree is if he feels he's witnessed a strong enough "sign for god" that it should happen. Cromwell himself was a man entirely committed to his own personal beliefs and morals, and to be honest it might be hard to have him interpret a 'sign' in such a way; it is however known that Cromwell let almost all his important decisions hang on 'waiting for a sign', which often resulted in his objections being vetoed on account of his time wasting.
Cromwell was religious but not stupid. He only took Lord Protector because he saw parliament was just as corrupt with or without a King. Even with it he had limited power. Claiming backing from God may be good enough for him, but it won't stop the political reality of shattering his own power base. Cromwell has no desire to plunge the country into war again, especially against the men he fought beside fighting the LAST King.
Title or no title, he had the power from the get go sense the army rallied around him and him only; it's certainly an odd thing to say when referring to a figure as monumental and game changing as Cromwell was, but he never really exercised the power he /really/ had, neither as Lord Protector or as the head of the New Model Army. In any case, do you think it would have increased or hampered the stability level the commonwealth was dealing with? would he be accepted by other royals as such? In any case Tumbledown Dick is still probably going to be an incompetent.
The Royalists were the ones who wanted to make him King. This will never fly with the majority of the Republicans or the majority as parliament. As you said, even as Lord Protector he never really hand any power. Something like only 2 or 3 laws were passed during his reign due to parliaments endless bickering.
Richard will always be stuffed. He isn't a good politician and he isn't a great military leader. No one rallies behind him and King or not his fall is inevitable.