Killing Oliver Cromwell early might help.
Without Cromwell, victory is likely more messy and the regime afterwards is likely to be more like the French revolution's Reign of Terror. There's a TL somewhere here where Cromwell is not involved in the civil war (not dead, he migrates to the New World and becomes a shark slayer!), resulting in a very crapsack England indeed.
A better, more stable Cromwell successor may pave the way for a better English Republic, but the army and Parliament were just not united, even within themselves! The so called levellers never had popular support for a more equal republic, many just see them as too radical.
And as long as House of Stuart has potential heirs, there's always the possibility of Restoration, especially with other European powers not wanting England to set a precedent. Hmm..maybe a bungled up restoration, but even then as in OTL, everyone would rather have a replacement monarch than a republic.
So the POD is going to need more than just the removal of Cromwell, heck his removal may be even more detrimental.