The definitions you present uses dubious logic. For example you say Republican Rome didn't have rule of law, since they (after lasting 450 years) turned into a dictatorship. And Iceland wasn't rule of law since the ended up being conquered by Norway. This means that if Britain at some point - however long into the future - turns into a dictatorship or is conquered by foreign power, then not only will this end the rule of law, it would mean that it never had rule of law in the first place, and some other nations must be designated as the inventor of rule-of-law! That is an ahistorical way of explaining history - I think the technical term is "whiggish history".

Also you are using a lot of "no true scotsman"-logic. Cromwell wasn't a true dictator since he still had to struggle with parliament. But the same is the case with the Roman emperors. There was an ongoing struggle between the senate and the emperor, and for example the senate deposed Nero, which shows he wasn't a sovereign dictator.