Mediators will generally agree that a principled approach to negotiation, where a careful analysis of the respective merits informs the attempts to find a sensible compromise, is likely to be more successful in achieving settlement than a positional approach, where a party refuses to engage in such analysis and bases the negotiation around a series of demands and/or threats.
If you choose the former strategy, it is worth using your position paper to set the tone and demonstrate your willingness to have a principled debate as the means of engaging the negotiation. It may even advantage you to submit your position paper in advance of the other party’s rather than by way of simultaneous exchange in the hope that the other side will adopt a similar approach.