Distribution implies a distributor; perhaps your paper might profit from some time investigating who or what it or they are and how they work.

It’s existence is justification enough for me. What’s the next question, “How do mountains justify their height?”

Life isn’t fair and any position can be “justified” if there is a strong enough motivation to do so. I’d recommend redirecting the question or looking to a specific instance.

I've thought a lot about property rights over the past few years, although maybe not from the perspective you are. Steer me toward some specific philosophical sources.

The heart of the matter to me is the question of what is the source of property rights and what role does society/government have in regulating them. In Massachusetts, USA, where I live, property legal rights are founded in a couple of original charters from the King of England in the 1600s. Theoretically, if you go into property records, you'll be able to trace deeds going all the way back to those. Easier said than done. It is my understanding that, as towns were given individual charters and rights to land, distribution was put into the hands of local committees which decided how the land would be distributed.

The important part of all this to me is that all property rights come from the government. There is no divine right of property. The granting of property ownership comes with obligations that can be traced back to those original charters. In my view, this gives the state an ongoing interest and authority over property ownership. This includes the rights of taxation and reasonable regulation - zoning, building codes, historic districts, environmental laws.

Government's authority gives it leverage to try to address the types of property distribution issues you raise.

I feel like unequal distribution of property is just the natural order of civilization. However, it can be debated as to what degree the inequality should be. A more just society might have lower levels of inequality, but I feel like some inequality is necessary for a healthy functioning society.

Sounds like a homework question that I can't help you with, as I don't recall what either would have said that might have amounted to their justification of unequal property distribution (I'm lucky at this point that I can recall that Aristotle's full name was Billy Bob Aristotle), but an easy justification is that (a) we require different people to do different things for society to function, and some of those things--like farming--can only be done via unequal property distribution, and (b) whether it's required or not, different people contribute unequally, and why shouldn't they be rewarded for their contributions? That's a major motivator, after all.

Well Locke believed that the interests of individuals would naturally work together towards the common good. Economic activity is virtuous, leading to better circumstances for all. If you have much property, then you can be more economically active, so inequality is not unjust.

I am not sure what Aristotle said about property specifically, but I think that he considered wealth to be a prerequisite for virtue.