(Why the quotes? They are explicit terms dammit! They don't need quotes!)
Regarding property rights - no, they aren't natural. They are recognised terms, if they were natural you'd never have seen the commons. It is enshrined now, and that isn't (IMO) itself a bad thing. However the concept of the Commons and unused land existed all the way (at least in the UK) till Enclosure.
Plus, Anarcho-Communism respects the concept of Personal Property, but not Private property - an important distinction IMO. I don't see how that is hypocritical since its a base position.
As for Anarcho-Capitalism, I think the idea is terrible, and self-defeating for exactly what you outline. It demands the end of a state, but Capitalism relies on the institutions of the state to function. However we've seen historically that private armies, private police forces, and private land agencies all have the power to become states in and of themselves. Private industry tends to try and monopolise. If the All-Green Police of New Mexico have an effective monopoly on force in the region. It all relies on the principle of non-aggression, ignoring that humans abuse power all the time. Hence why it is the most likely to appear, but also collapse. I guess we agree there
Minarchism makes more sense - but the reality is that if all it does is protect private property (basically the Night-Watchmen State in practice), it ignores all sorts of other abuses that we developed a state to address. Everything from sanitation, to common standards, etc. Which leads to my biggest issue with Libertarianism. It tends to be a naive ideology that has no method to address bad actors. Further, in Democratic states, it completely ignores that the Democracy IS a system of self-governance. It is why you see a peculiar political trend of "Libertarians" moving to "Authoritarians" rather rapidly, because the reality is not that they want localised power, but they object to the decisions that have already been made. There are good-faith Libertarians, but considering that tent is already used as a thoroughfare I don't see it capable of building a functioning society that won't be steam-rolled.
In contrast, the equivalent to me would by Syndicalism, which does address a whole mess of these principles.