:::I think you are too hung up on official titles (which are not commonly used) and splitting the articles up that way is less than helpful (because AFAICT most secondary sources do not). For example what is much more important in English politics  particularly in the second period of the commonwealth was which if any parliament was sitting. For example once the Rump was recalled all Scottish and Irish MPs were excluded from power and besides the Irish MPs that did sit in the Protectorate parliaments were were frequently NMA soldiers.