Since this thread was reference elsewhere. Belloc did "evolve" over time, and ended up more monarchist, but I think that the radical monarchists often deride those who oppose the absolute and hereditary monarchies that fell into place.
St. Thomas Aquinas even outlined the problems with a hereditary absolute monarchy, where simply inheriting a right to rule means that you often have inferior rulers, and absolute unchecked monarchy leads to tyranny and also to tragic situations such as in England where a rogue heretic / apostate monarch dragged the entire country into heresy.
I hold that there should be an autocratic rule but subject to numerous checks and balances ...
1) Constitutional Restrictions
2) Country's Catholic Bishops could Veto any decision, action, or legislation that the Autocrat attempted to impose on the grounds of their violating Catholic principles ... but the autocrat could appeal to the Pope in case he believed the bishops were wrong
3) There should be an aristocratic body, like a House of Representatives that could veto legislation, actions, decisions based on other reasons unrelated to Catholic principles, such as whether they were prudent or imprudent, would benefit the country or not, and in particular the part of the country they represented. Unlike the US system, this body would not make decisions or legislation, etc. ... but would only be in a position to veto the decisions of the autocrat, and perhaps this is where you'd need a 2/3 majority to exercise a veto. This would be to protect people from burdensome, onerous, or imprudent activity
So, the candidates for the House, the aristocrats, they would be elected by the People, but before being eligible for election, they would have to be approved by their local Bishop, and would Constitutionally have to be practicing Catholics, considered devout / devoted to the faith, and should also have to pass at least some minimum intellectual requirements (focusing on logic, philosophy, and other subjects). Once certified, the people in a region would vote for their Candidate.
No Candidate could spend any money to run for office or to buy/win influence. Each candidate would be permitted equal time to advertise his positions and platform and make a case for himself, perhaps on some website or whatnot, and the people would be required to familiarize themselves with each candidate before voting.
Voting would be limited to men, who are certified by their pastors as being practicing Catholics, but each man's vote would have weight according to the size of his household. So if a single man voted, he got one vote, but if a man with a wife and 10 children voted, his vote would count for 11. All this would have to be certified beforehand also by the priest (or a deacon). This would limit the influence of emotional voting, but nevertheless, if various questions such as whether or not to declare war came up, or various economic questions ... a bunch of single guys or DINC types would not be able to vote for economic measures that favored them over those with large families or vote to go to war when they were too old themselves and would be sending other people's children to go die.
In order to limit the pool, perhaps a committee of priests along with a bishop might pick the top 5 candidates in any given region as being allowed to run for office. Perhaps candidates would be limited to those who had been Catholic for a certain number of generations, to limit the possibility of infiltrators faking conversion just to infiltrate the political system.
Then, the aristocratic body could vote among themselves for who to elect President / Autocrat, etc. -- for a reasonable default term, perhaps something along the lines of 4 or 5 years. But in the case of lost confidence, the aristocratic body could vote him out with a 2/3 majority, and then hold a new election.
There would be no "Parties" or any crap like that which might be used to manipulate votes. There would just be one "party", a Catholic "party".
This would address nearly all the issues with hereditary absolute monarchies, where a monarch could become a tyrant, or be some moron who rules just because he's in the blood line, where there he would be checked by a Catholic (Church-approved) Constitution, as well as by aristocrats, who met certain religious and intellectual requirements, and thus are aristocrats, and not influenced by wealth where it could turn into a plutocracy, where elections could be "bought" by paying for influence. You'd have to make illegal and disqualifying any attempts to "buy" or "canvas for" votes. You would make a presentation, recorded speech, provide a written platform, be required to be certified by your pastor as a serious, credible Catholic (of several generations) as well as passing exams for intellectual capability (ability to reason). From among these would also be elected the President. Even voters would have to be practicing Catholics, would get weighted votes based-on the size of their households, women would be excluded to prevent emotionally-driven voting, and the voters would have to pass some very minimal quiz at least to indicate that they studied the choices somewhat and weren't complete morons.
No Plutocracy, no Jewocracy, a Catholic Constituionally protected form of government subject to vetos by the Church as well as by the aristicratic body, etc.
IMO ... perfect form of government.