I think it would also help if you killed/captured a lot of the main Stuart Pretenders. This being Charles II, James Duke of York and William III (getting rid of his mother is easy enough.)
Now you could have Charles II captured, as instead of diverging from the main party that got captured he could instead go with them and be captured.
James, Duke of York could be dispatched of during the Battle of the Dunes.
Mary, Princess Royal catches smallpox from her husband and, due to her being weakened from the pregnancy dies soon after, the child isn't born or if he is then he won't survive.
Now you have a scenario where the only real contenders are Henry Stuart, Duke of Gloucester who's looked after by the government and in OTL seemed pretty loyal to Parliament. And the others are of course the German line, this will either (IMO that is,) lead to no succession. Or a bitter relationship between the Commonwealth and the Palatinate of the Rhine.