As far as re using the factory wires it might be possible but its going to require a lot of cutting into the stock harness. You'd need to intercept the wires and bring them to where your amplifier is located some how. It's probably much easier to just run wires to your speakers. Depending on the power your running to can get away with a very small gauge wire 16, maybe 18 if you don't feel like listening to social norms.
I'm interested as to how you are going to disable the fixed EQ. Link to the post?
Also how are you going to run your amp, Highlevel inputs? You'll need to figure out how your going to get signal from the stock HU to your amplifier.