We urge you to clarify with your congregants that they accept the following rules of engagement, which are important for both halachic and practical reasons.
In such a dispute – which is of only moderate financial scope, but which can evoke significant personal feelings – the sides should assure you that they will not allow the dispute to develop an adversarial bent. Your impression is that (most of) each side’s claims have logic. The two sides should realize that this is not a dispute between right and wrong or good and bad, and they must not be overly embarrassed, upset, or even surprised if they are not as vindicated as they expect. It is not shameful to be somewhat off on matters of fine legal distinctions or careful analysis of what transpired, and it is meritorious to accept a decision arrived at sincerely and to do the proper thing vis-a-vis one’s neighbor. Money lost in such a situation due to payment to one’s counterpart or receiving less than expected is no more of a loss than the higher cost of kosher food or needing to pay tuition at one’s children’s schools of choice.
Hammering home these ideas is important for at least two reasons: 1) These points are true and educational, and this is the right time/setting, as their rabbi, for you to teach or remind them the proper mindset regarding conflict resolution. 2) If they have an adversarial approach, you are likely to incur resentment from either or both sides for not living up to their expectations.[1] Since you will need to interact with them communally and personally, you do not want to harm relationships. Therefore, if they do not have the proper attitude, we recommend referring them to a different framework.[2] Working it out themselves is best, but if they are not able to accept the peace-loving approach to settling the dispute, it is unlikely they will be able to work it out themselves. Mediation[3] or a formal beit din are often good options.
Next, let us examine your role. Due to a few points, we suggest that you not view or present yourself as an ad-hoc dayan, bound to a Choshen Mishpat[4] ruling. First, as you yourself point out, you have not had sufficient training and practice to rule proficiently. Furthermore, arriving at the correct ruling may be very time-consuming. Seeking assistance from dayanim[5] minimizes these problems, but it is not an ideal situation.
In addition, under ordinary circumstances, monetary decisions are rendered by a beit din of three dayanim, not by a lone dayan.[6] Even a special expert, who is entitled to serve alone, should generally try to avoid adjudicating by himself.[7] While it may be permitted for one to do so when the litigants specifically ask him to, it is still not ideal.[8] The best solution is to say that they should accept in advance a ruling based on your reasoning, which might be according to Halacha but which also might possibly be a halachic mistake.[9]
Another issue is that you have already met with each side separately. Such meetings can be helpful when dealing informally with disputes, but it is forbidden for dayanim, both according to Halacha[10] and according to arbitration law, to hold such meetings. It is permitted, however, to adjudicate even in such a situation, if the sides agree to it.[11]
All of these factors push toward the preference of giving up on the dayanut route in favor of less formal dispute resolution, which the gemara[12] refers to as the approach of Aharon (as opposed to that of Moshe). If you can serve as a mediator rather than as an arbitrator,[13] that is ideal. If they need you to make the decision, then to the extent that Halacha guides you as to what is fair and logical, that is great. However, the sides should expect a ruling based on p’shara,[14] and not necessarily one that is based on formal legal/halachic grounds.