You are totally right about the Sign of Peace being oddly placed...it should be at the Preparation of the Gifts, where it was intended to be placed...you know, the Scripture, "if anyone remembers that he has a quarrel with his brother, he should leave his gift and go and make peace with the brother." There was apparently some back and forthing on the issue, and it ended up where it is...but you are right...and perhaps we should expect it to be changed to make more sense. I see that Pope Francis is asking for some work to be down on the "New Roamin' MIssile" (sorry, my joke) so maybe there's hope!