Actually I have to agree - it feels like the narrative has moved beyond the need for Littlefinger to come back, so I doubt we'll see it happen.
Still, he knew Bran was on to him when Bran told him "chaos is a ladder." A short time later, Arya returned to Winterfell, revealed herself as a spooky assassin, and started giving Littlefinger the stink-eye. It would have been in-character for him to leave at that point so he didn't get caught in a trap.
Leaving would have been difficult (because if he leaves, presumably the Vale leaves with him, which wasn't going to happen). The Faceless Men angle was an elegant way out, even if I doubt it is going to happen. As for the love-for-Sansa motivation to stay - I don't buy it. This is a guy who just married her off to the Boltons. He didn't love Sansa, she was just another pawn on his board.
In his own way, he did love and want her. And since you like chess analogies, yes, she might have been a pawn, but she was the pawn that he aimed to turn into his new queen, having lost his original one (her mother). You don't think that he'd come "rescue" her at some point when he'd feel powerful enough?
On the contrary, he was a very active instigator of the Stark-Lannister conflict. The death of Jon Arryn brought Ned into King's Landing, as Baelish knew it would. While Ned was Hand, Baelish was actively convincing Ned to commit resources against Tywin in the Riverlands. And in the end, Baelish convinced Ned to organize against Joffrey, promising the City Guard's support. And then he put a knife to Ned's throat and betrayed him, resulting in Ned's death at Lannister hands. After that, Robb was declared King in the North and the war began in earnest. Chaos is a ladder.
It was Robert's death first and foremost that allowed things to get out of hand, followed by Ned's. So I stand by what I said, as those events couldn't have possibly been a realistic part of whatever he had hoped for with the Arryn thing.
Drax the Legend, Captain of the Fist, The Starwalker, The Jade Slayer
Littlefinger was feeding Ned info about Robert's bastards all through season one, which was leading Ned to the realization that Robert's kids were really Jamie's kids. That put Ned on Cersei's radar and accelerated her murder of the king. Littlefinger really did start it all. He may not have intended for his actions to result in Robert's murder, but he sure didn't mind.
The only cause of the war he didn't influence or predict was Jamie's attack on Bran. But he capitalized on it by helping Joffrey with the second attack on Bran.