I don't think Anakin got lucky, I don't think any such thing as luck in the Star Wars universe. Anakin used the Force without realizing it and Luke did the same thing. Even Han told him that shot was one in a million.
Luke did realize it though. He was deliberately trying to do exactly what the Obi-wan voice in his head told him to. How could he do that without realizing it.
I don't remember if Qui-gon dies before or after the ship is destroyed, but if it was before or was changed to be before we could have had the same sort of scene with Qui-gon telling Anakin to use the force. It's like poetry. They sort of rhyme.
Qui-Gon is fatally wounded at that point, but sitll alive.
The thing with luck though, is R2 is lucky. If Jar-Jar hadn't delayed him on his way to fix the ship, he'd have been quicker up the shoot, probably shot off with the other droids.
Anakin's control of the fighter is at least covered by dialogue - it's remote control. That makes sense to me. Why programme several flight paths when one will do. Follow the leader. R2 disables it, then R2 is flying. If anything R2 should know more about the ship, he's designed for it!
Even Obiwan says flying is for droids.