Well, the OP says that the POD could be anytime from the beggining of the Seven Years War.

So a different war is allowed.
So the question is, how does the war need to chance to make this a possibility?
Obviously, Peter needs to stay in control. I would say that Prussia needs to come out with a stronger performance overall, but given how badly they were being beaten in OTL before Elizabeth died, I'm not really sure how to do this. Maybe the war is simply an indecisive draw for all concerned?
Here's a thought: Have 1759 go in some very different directions. A french victory at Lagos (say that de la Clue is able to take advantage of Boscawen's divided command, defeating him in detail) causes some butterflies, cumulating in an attempted invasion of Britain (different analogue for Quiberon as well, perhaps?). The french score major successes, pushing the british to the limit, but are unable to knock them out of the war. Meanwhile, Kunersdorf is a drawn battle, and the french continue to have poor luck in germany. Maybe knock the Swedes out of Pomerania as well. Instead of the Prussian near-collapse, their war with austria and russia continues to be an indecisive duel, while France, due to distractions regarding england and poor showings in Germany, cannot decisivly intervene. By the time Elizabeth dies, England is in serious trouble, enough that it cannot really keep its allies and itself going, France is still powerful there but weak in germany and weary in general, Prussia is on its last legs but still relatively intact, Russia and Austria are unable to decisively defeat Frederick in the field, and the Swedes are in some way or other out of the war. Peter's desire to end the war may well result in a general peace by exhaustion.