I've ALWAYS believed the endgame is
Jon Snow legitimized as Jon Stark/Targaryen with....Daenerys Targaryen as his queen....and Tyrion Lannister gets the Westerlands and Castlery Rock.
I don't know how Tyrion does it, in some way he ousts and tricks and overthrows all the other Lannisters and pledges loyalty to the Starks and/or Targaryens and ends up ruling his families traditional lands.
I don't know why, but I always felt this is a story about coming from the bottom, having nothing and rising to the top and those three started with NOTHING.
Jon Snow - a *******, outcast, vows to protect the realm, selfless, honorable family, great fighter and fearless, never surrenders.
Daenerys - started in Essos with nothing but a name, some dragon eggs and supreme faith in her bloodline, building an empire one battle at a time and learning it the hard way
Tyrion - an imp, an outcast of his own family, but smarter than the rest, a survivor and more knowledgeable in battle than many give him credit for and in royal history than almost anyone.
As for Targaryen marrying Targaryen in the case of the Rhaegar/Lyanna theory for Jon Snow - thats not uncommon for Targaryens - it was common practice in ancient Valaria. Heck Daenerys parents are brother and sister. And Viserys wished Daenerys had been born earlier and could have married Rhaegar instead of Elia Martell.