Getting the Doctor to steal the right TARDIS would appear to be the only time she consciously interfered with things. In Asylum and The Snowman she only seemed to have an inkling of her real self on the verge of death.
I suspect some instances of her intersecting with the Doctor required more action than others.
Thinking about that, it opened another can of worms in my head. Ask yourself, how did Clara know which TARDIS the Doctor should steal? It's Galifreyan technology and looks no different than any of the other TT capsules. With the TARDIS' history of rejecting/disliking "impossible" companions. Such as Clara and Jack Harkness. I think it's unlikely the TARDIS communicated the specific information about itself to Clara so that one of her millions of copies would know to influence the Doctor's decision about which one to steal.
I think it was in "The Deadly Assassin" or "Logopolis" when the Fourth Doctor says he stole the TARDIS when she was in for maintence. In "The Doctor's Wife" the TARDIS herself says she was a museum piece when the Doctor stole her/she stole him.
I don't really mind the inconsistency of copy Clara's memories regarding their mission to save the Doctor. If suggesting the Doctor pick the correct TARDIS was Clara only conscious action of countering the GI interference, I'm totally down with that.
Just to throw another spanner in the works, what if the Tardis Clara told him to take wasn't actually the Tardis we know and love, maybe that's why the Tardis was always trying to shut Clara out!
Here's a mindscrew for you. We see Clara on Gallifrey, but presumably she is still biologically human. If she went to every point in his timeline, she must have been there right at the beginning of his very existence.
What if one of the things she did to ensure his safety was to create him in the first place, Emissary-style? What if, not knowing the significance of her actions, she shagged a Gallifreyan bloke and gave birth to a baby?
That would make the Doctor half-human, on his mother's side.
You know that's quite a scary thought