[EVERYTHING] Possible reason why Littlefinger needs Sansa?

So, we all know that Littlefinger is the hypercreep around Sansa, but he might have a reason to try to marry her other than being a creep. We know that Littlefinger was a the Tourney at Harrenhal, where Rhaegar Targaryen gave the winter roses to Lyanna Stark rather than his wife, Ellia.

Lyanna was said to be "raped and murdered" by Rhaegar, but actually they had a child, Jon Snow. In this scene: https://youtu.be/Bfnl9owFc84?t=2m10s everything except Jon's parentage is revealed. At that timestamp I linked, it seems as though Littlefinger was going to say something to correct Sansa, about the rape and murder. I believe that he knows Jon Snow may be a child they had, giving Jon a strong to the Iron Throne. If Sansa marries Petyr, then if Jon has no children, and dies "accidentally," that would give Littlefinger a strong claim to the Throne through Sansa.

TL;DR: Littlefinger wants Sansa to marry him because he knows Jon has a claim to the Iron Throne. After Jon is murdered somehow, that would give Petyr a claim to the throne through Sansa.