I have read that Pope Pius VI called monarchy the "best form of government". Is that accurate?
I'm not familiar with the citation. It certainly isn't the dogmatic teaching of the church. Popes can have private opinions that aren't binding on the faithful, and can teach in ways that are not binding on all Catholics for all times to come.
Obviously, heaven is a monarchy, and so is the church. But the monarch in heaven is God (who is perfect), and the monarch in the church is a representative monarch whose powers in the spiritual realm are actually rather limited and whose powers in the temporal realm are absolute, but only over a country the size of a city park and a few hundred subjects. It's not clear that either heaven or the church are an ideal, or only, model for a civil polity.
Switzerland has been a republic since the middle ages, and has been majority-Catholic the entire time, and the Church has never had much of a problem with that, nor has she had any problem with getting the Pope's own bodyguards from that republican nation.