First of all, we have a problem giving advice that could afford you a monetary advantage at someone else’s expense. The mishna in Pirkei Avot warns us to avoid being like orchei hadayanim (translated, in modern Hebrew, as lawyers). There are different opinions exactly when this applies.[1] Our policy, as a service dedicated to helping Jews further their Jewish knowledge and practice, is to not take sides in disputes between litigants, as honorable as either side might be.
The next thing you need to understand is what “I am better off” should mean. While society, in general, concentrates on how to get every penny one can, the Torah teaches that it is at least as important to pay every penny he owes. Now, it is true that when one is not sure whether he owes money, the halacha often is that “the burden of proof is upon the one who wants to extract money,” and the one who is “holding on” need not volunteer to pay. However, if the defendant knows he owes the money, he is obligated to pay everything he owes unless the plaintiff relinquishes his rights.
P’shara, whether by means of arbitration or mediation, is the best way to solve a conflict.[2] Even a beit din (rabbinical court) that is requested to adjudicate should try to convince the parties to agree to a compromise.[3] However, that is the case as long as each of the litigants believes that he is (or, at least, is likely to be) correct. The Shulchan Aruch[4] rules: “Someone who has been demanded to pay money is forbidden to search for means to avoid paying in order that the other party will agree to make a p’shara with him and relinquish his rights to the rest of the money.”
Realize that if you want us to look into the facts, as you present them, we cannot assure you that you deserve to win the case, as we do not know how the other party would respond to your claims. We might, though, determine that, even according to your version of the story, you are responsible for some or all of the disputed funds. Then you would be bound to pay what you owe, and a p’shara would not be possible for that portion of the money. You would be responsible to inform the other side how much you concede, so that any money he would relinquish through compromise would be based on informed consent, not ignorance.
Although, as mentioned, one must normally pay that which he knows the beit din would require to pay were it to adjudicate, there are exceptions. For example, if you are correct, in principle, but are unable to prove your claims, then you could take certain steps to pressure the other side to a p’shara rather than simply lose the din Torah.[5] Other circumstances and steps are discussed[6] but are not all are clearly permitted. You are permitted to appeal to your counterpart’s sense of fair play and to encourage him to go beyond the letter of the law. This would justify telling your counterpart that, although halachically you have to pay (if that is the case), you have claims that strengthen your side morally. This is permitted even after a formal verdict of the beit din has been handed down.[7]

Outcome: The student requested that we try to determine his status. Based on his story alone, he seemed to owe at least most of the money [details beyond our present scope]. He informed the other side of this and appealed to him with a variety of claims; they reached a gentlemanly compromise somewhere in the middle, to the satisfaction of each.