Bingowings said:
Perhaps there should be a 'finding Anakin' subplot, another possibility is that the Jedi know that the Chosen One is out there somewhere. Qui-Gon has a premonition that assisting in the Naboo crisis is the key to finding this child and unlocking the meaning of the prophercy, which is clearly important to them and for the greater good (they just don't know how much damage has to be done before the galaxy receives the boon that the child represents). "I Have encountered a vergence in the Force", becomes "I sense a vergence in the Force".

Qui-Gon hasn't met Anakin yet but he foresees he will so the council send Qui-Gon and Obi-Wan to investigate the invasion and hopefully bring the Chosen One back with him.

Such a plot alteration would place Anakin further up the map of the story and foreshadow the rather wobbly way the Jedi deal with him in later life.

I've thought about going in that direction too. Sidious sends Maul to Tatooine to look for this "vergence" he senses in the Force, instead of the Queen. Meanwhile, the Council sends Qui-Gon. It's a race between the Jedi and the Sith to find Anakin first.