You must accept that property rights and the non-aggression principle are fundamentally incompatible for two reasons.
First, all property was acquired through violence and therefore must be declared NULL AND VOID in a society which will truly honor any non-aggression principle
Second, unless you will begin your new society by SEIZING all property and redistributing it EQUALLY to all people of Earth, you cannot ENFORCE property rights, which presuppose wealth inequality, without systemic use of coercion and violence, AGAIN violating the non-aggression principle.
Wait, are you merely advocating for no property rights in regards to land property and the means of production or all property including personal property?
I have already addressed the nuances with land property and there doesn't need to be any land redistribution through violence as most land is uninhabited and owned by the state(an entity who lacks rights that I acknowledge).
The reason capitalism and non-violence are incompatible is because capitalism IS inequality, and inequality IS violence. Without systematic top-down hierarchical violence, society would very rapidly return to the homeostasis of relative equality.
I have already acknowledged the existence of structural violence in capitalism and even went so far as to argue your point for you while you have yet to admit the inherent violence in your proposals.
Would you call a starving person taking food to feed themselves a violent act? If so, you are a fool and not worth debating. If not, you have just forfeited your entire argument about property rights in a society of non-aggression.
Theft is indeed breaking the Non -aggression principle even when a homeless person commits it. If a homeless person asked for food I would willingly give it. If I wasn't around and he stole it to insure his survival I would understand and be fine with this act (even though it is breaking the NAP) as long as he acknowledged it, thanked me, and offered remuneration (which I would likely turn down and gift him what he stole). Anarcho-caps are humans too and not sociopathic assholes as you want to pigeon hole us into. I am sure you a a nice person with good intentions as well.
Taking property is not violence. Hurting human beings is violence. Letting human beings starve is violence. Letting human beings die of exposure is violence
I would be interested to learn if an anarcho -communist society could solve these problems you are attempting to cure. History has not been kind to anarcho-communists, but perhaps you have the magic formula to make it happen? I encourage you to pursue your dreams.