PT Assassination Attempt on Amidala in Episode 2

Why doesn't Zam just shoot her through the window? We know she has good aim.... Or even Jango could've flown up to the window with his jetpack and shot through the window and killed her. I figured the reason they released the kouhuns into her room it's because they were trying to kill her discretely and not get caught doing it because if a blaster shot was fired, everyone would hear it and they would get chased after. Any thoughts on how Jango and Zam could've executed this plan better than what they did?

 

Jango wants something more subtle, after Zam's rather public failure on the landing pad.

 

Yes he specified subtle, drawing attention by such a blatant assassination attempt makes way for a possible escape, or witch hunt for her. Being subtle makes it easier to avoid detection and should have made it far more likely that she couldn't possibly recover.

And besides Zam wasn't outside the window, it was a droid that's only function was to dispense the poisoned worms.