I know that there's been discussion that River probably couldn't be Rose because (1) the writers who respectively introduced the two were different and (2) Rose is in the parallel universe with meta-crisis/human Doctor. There's just something that I wonder...
River's quote about the finest man that she ever knew reminded me of Rose's quote in 'Father's Day' about how Pete was the most wonderful man in the world. (Beware of spoiler if you haven't seen the Father's Day and/or Doomsday episodes yet!) Remember how, while Rose had saved his life when he really would have been killed,related events caused a tear of sorts that let monsters come and kill, including the Doctor? Pete stepped back out in front of the car again intentionally to undo the damage, bringing the Doctor and others back to life? That was the first time that we see him as a hero. Then there was the scene in Doomsday when he stepped in just in time to save Rose from being swept into the vast nothingness (sorry--I don't remember what the official name that it was called). He was always watching out for her.
Now, I know that the human Doctor was supposed to take the real Doctor's place with her in the parallel world. While the scene was taken out of the final televised version, the DVD shows a cut scene in which the real Doctor gave the human doctor a piece of the TARDIS so that that human doctor could build a new one and travel through time with Rose. In later commentary, the writers said that one could assume that this could have happened in the storyline had it not been removed. Rose worked for the UNIT and a storyline could have supported that she could have continued time traveling but with the human doctor instead of the real doctor. Remember, though, that the human doctor only had one life. If he was mortally wounded, he wouldn't be able to regenerate. Then Rose would have found herself again without the Doctor in her life.
Here's where the Pete/finest man quote could tie in. If Rose tried to find the Doctor again but fell into danger, Pete would have tried to save her if he was around, whether it would be from protecting her from something or trying to keep her from going at all. Or he may have sacrificed himself for his daughter's happiness. I don't think that she would have killed him as in murdered him. Consider, though, how people blame themselves when someone they loved dies. If he had been trying to protect her or if, like in Father's Day, he died as a consequence of something she did, she may feel that she had killed the most wonderful man in the world/finest man she ever knew.
How could she have turned into River Song instead of the Rose Tyler that viewers recognize Billie Piper)? That may have been something that the UNIT was connected with. Also, while the 10th Doctor removed the Time Vortex from her, could it have had a residual effect on her?
I see the logic in the theories that River Song could be the original Mrs. Doctor, the Doctor's mother, or the Rani. I've also heard theories that the Valeyard that the 6th Doctor faced may return and that there may be a show down between the human doctor and the real Doctor. Could Rose have had changed her entire identity to hide from an evil human doctor and to find the real Doctor? I realize that all of these things may be a stretch of the imagination but the writers have been known to surprise us and, from what it sounds like, they may surprise us again.