Alright, I will rebuttal My openings statement and then my opponent will do the same to my opening statement. Let dive in.
Moral Particularism claims that no values are universally true. It also claims that no actions are universally good. Moral Particularism is not "The Best Possible Model for Morality".
Well we're on the same page as far as definitions go. Score one for us. No lets see what the "best possible model is?
Utilitarianism: an ethical theory that determines right from wrong by focusing on outcomes. Utilitarianism holds that the most ethical choice is the one that will produce the greatest utility for the greatest number. 
To me, utilitarianism is just an outdated version of moral particularism. It still does things from a situational standpoint but appeals to utility as it's highest standard. Things like the trolley problem and the doctor problem actually show the inferiority of this position. Particularism still makes appeals to utility, however, the key difference is that autonomy can and should be placed higher on the priority.
This is why a doctor cannot harvest the organs of 1 person to save 5 people. To do this would be an appeal to utility and it's one that is rejected by society and most moral philosophers historically.
In short. Moral particularism is still better than utilitarianism because it's less restrictive about how utility should be applied. Although I respect the idea of utility by itself when it does not step on the toes of autonomy. For this reason, I would be inclined to reject any model built off this idea as being the highest one.
Also, I believe the only real two solutions to the trolley problem is either for the person to stop the train and kill themselves (appeal to autonomy) or to simply admit that you cannot make the right decision because you have no way to appeal to one life or lives being more important than another (appeal to autonomy) Save 100 kill 1 doesn't generally work in most situations. What if the single guy on the trolley is the next world hero and will save millions? How can I know? What if the group of people are suicidal and the singular person had a zest for life? There's no way to sort out the autonomy or the utility of the matter accurately, this means that the conductor can only appeal to their own autonomy and utility. The fact that I can change around the variables of the train problem and get different candidate options also shows that their are particulars at play here (score)
Utilitarianism values life. It argues that Genocide and extinction are bad because they decrease life/happiness (however, they can be framed as good in the rare case where genocide/extinction would ultimately maximize life/happiness). Again we can use utility as a universal basis for morality.
While this idea looks good on paper, in real life there is little to no situations where the utility of the matter can be sorted out. For instance, we have no way to know if another Hitler is going to arise until he already kills a bunch of people, at which point, the utility appeal was a tad late to the game. Of course, since HItler was violating the autonomy of millions of jews, it logically follows that we can appeal to their autonomy over the autonomy of HItler and take him out after the fact. So there is no need for utility appeals here.
How can we determine what constitutes absolute right and wrong? What this argument really boils down to is Moral Absolutism. Moral absolutism asserts that there are certain universal moral principles by which all peoples' actions may be judged. 
I would agree that there are certain "objective" principles going on within evolution, such as harm/benefit. Fair/not fair. etc. But I don't see these things as being universal.
To be universal would mean that everybody has these inclinations without a single exception. Since things like sociopaths and alternative societal moral systems exist, it makes more sense that we're working on an objective standard that is part of our random gene mutations. This, in my opinion, is the only model that accounts for the near universal nature of morals while also explaining the exceptions.
The principle of moral supervenience states that moral facts are a function of reality, of the natural world . For example, should Bob pay me $10? Well, that depends on non-moral facts, like, did Bob buy something from me? Does Bob owe me a debt? We base our morality on non-moral facts.
Ahh, but you're not citing universals right here, you're citing particulars. If it's "should bob pay me 10?" in universalism, then the answer is always yes or no. But in particularism, which is the polar opposite, Bob's debt is decided by the particulars.
The only way a moral is universal is if you have all the particulars first. So I can't say Bob should pay me 10 dollars every time. All I can say is that Bob should pay me 10 dollars every time scenario X arises. That's the key difference here. (good job bob)
In summation. I would say that me an my opponent are not far off from each other and the real argument is over methodology.