What seems like a long time ago, Pope Benedict XVI asked for thought to be given to moving the Pax to its 'Ambrosian' position before the Offertory, so that the Lord's command (be reconciled with your brother before you bring your offering) can be obeyed. But I wonder if we are being a bit too quick in assuming that the Roman position is secondary.
Remember Dix's point: "Unless we recognise the important change produced in Christian theological method by the definite canonization of the N.T. Scriptures, which only begins to have its full effect after c.A.D.180, we shall not understand the second-century Church" [Jurisdiction pp117-8]. And don't ever forget the immemorial antiquity of the Roman Rite, older than any other liturgical tradition, older than the time when the New Testament Canon was settled (another Dixian point). A Roman custom is not to be sneered at for being "late"; it might be earlier than biblicising fashions which started to circulate in the third century. So perhaps the 'Ambrosian' position was introduced later, when people had begun to tinker with Liturgy to make it "fit Scripture" better.
Clergy may explain the Peace variously. They may, for example, draw the attention of their people to the words at the end of the Our Father about the Lord forgiving our trespasses as we forgive the transgressions of others. Fair enough, Father. Edifying. Good stuff. But it's not the (historical) reason why! So I do think that there is a lot to be said for the clergy, at least, themselves to know the real reason why the Roman Rite does things the way she does.
We have the Magisterial authority of Pope S Innocent I to help us. The people of Gubbio (Iguvium), an important town some distance North of Rome, had been nagging their bishop to move the Pax from the 'Roman' position to the 'Ambrosian'*. The Holy Father [PL20, 553 or 56,515] explained to him: "The Peace has to be done after all the things which I am not allowed to mention [i.e.the Consecration] to show that the people have given their consent to everything which is done in the Mysteries and celebrated in Church, and to demonstrate that they are finished by the signaculum of the concluding Pax". And Tertullian [PL1,1171&1176-9], speaking about the ending of the Prayer, uses the phrase "assignata oratione": "When the Prayer has been sealed". The imagery is of somebody writing a letter or an agreement on a wax tablet and then pressing his signet ring down into the wax so as to seal, confirm, what is written. Tertullian asks "What Prayer is complete when the holy kiss has been torn from it? ... What sort of sacrifice is it, from which people go away without the Peace?" And other early writers such as Justin [First Apology 65] and Origen [PG 1,1282] bear witness to the belief that the Kiss "seals" a prayer which has preceded it. So the Pax 'seals' the Consecration and the Oblation. And, importantly, it has nothing to do with being chummy to ones neighbours. It is a sombre, almost legal**, business; more like signing a will or a bill of sale, than like greeting friends in the pub.
If this were realised, there would be fewer complaints that the moment between the Consecration and the Communion is not the right time to socialise (people are right! It isn't!).
I am glad that the proposal of Benedict XVI was not followed!!
*I suspect there is significance in the fact that the Pax was already in the Roman position at Gubbio. The 'Ambrosian' position looks to me like a spreading fad which was threatening an established practice. We get no hint in S Innocent's words of an awareness that the Roman position was an innovation; this would in any case be surprising, given the conservative and archaic habits of Roman Liturgy. And possibly even the 'Ambrosian' position may originally have had the purpose (see Justin) of sealing the prayer at the conclusion of the Missa Catechumenorum, rather than of expressing reconciliation before you make your offering.
** Remember the very 'legalistic' instincts of Roman Liturgy; in the Eucharistic Prayer we actually ask God to make our Sacrifice 'adscriptam' and 'ratam'; 'written into the list' and 'ratified'!