While I don't have a particular care which way a parish chooses to go, regarding your comment I will simply ask if your consideration of the communal nature of the forgiveness, expressed in the Lord's Prayer, doesn't simply preempt the Sign of Peace, which closely follows.  It would seem, to me, that one of the gestures (hand-holding or glad-handing) is made redundant by the other.
Isn't the communal nature of the prayer our communion with God, and the "forgive us" a plea to Him and not of the "other".