You can't just hack an AI, especially one that is eons more advanced than you to the point where its status as an entity might transcend your very understanding of it. Personally, I think it's a cop out to have any kind of hope for conventional victory. Even if you were to miraculously beat the few hundred Reapers over Earth, you still have thousands more of them in the galaxy, and they are going to know what happened, and they are going to be pissed.
Perhaps we can't hack an AI, but perhaps civilizations across time have created a device that would be able to do so. Obviously this would be massive to be able to deal with the complexity of the hack, it could be as large as a space station. See where I'm going here? The Crucible could have given access to the AI that controls the Reapers, rather than giving us the options of Destroy, Synthesis or Control, we can win on our terms, send out Code to drop their shields and allow an all out attack on the Reapers in such a way that we can win. And, just like in the ending cutscenes, the code would bounce through the relays to every Reaper in the Galaxy. Now, just imagine this from War of the Worlds:
https://www.youtube....CHHv7ojfiw#t=43
But on a Galactic scale. The Krogan on their homeworld, under severe attack, suddenly notice the shields have dropped. The word goes out, a full out offensive commences, the ships of the Armada swoop in back on Earth. And with you standing in the middle of it all, you could orchestrate the counteroffensive from your view of the open sky on the Citadel. Much better ending, if you ask me.
Edit: Just a bit more. You could have it appear as though nothing has happened. The Crucible docks, some sort of energy burst goes out but the Reapers seem unaffected. The tone changes, the one hope was a dud, Admiral Hackett stating that the battle is over, hold fire and retreat, someone fires a missile off in frustration.. tracking.. tracking.. massive explosion as it hits the Reaper. Moment of stunned silence, then the comms go crazy as everyone starts issuing orders to assault them now, that the shields are down. Meanwhile, on the Citadel, the starbrat is having a hissy fit, trying to convince you to stop the assault, that the Reapers are special little snowflakes meant to preserve the Galaxy against hokey rogue AI, that you're dooming everyone, blah blah, shut up starbrat, we win.
Dammit Bioware, so much missed potential.