I don't really don't see how Littlefinger is winning right now, or what his game plan is. None of the Starks trust him. He really overplayed his hand with Jon, who nearly choked him. None of the other houses in the North like or trust him. Sansa seems impervious to anything he says. Is he just wasting his time there?
Any chance of Littlefinger taking the throne was ruined when he left the capital in Season 3.
He's only visited again once to see Cersei and Olenna.
I can't see how he can take it with so little episodes left. He feels like a spare part nowadays.