using factory speaker outputs

Yes this works in most situations.  It is a trick that installers use all the time.  In fact, you may look into some "9 lead wire, or sometimes called speed wire." you may even find it even easier.  it is a single 4ga shielding with 9 individual wires inside.  the 9 wires are individualy shielded and color coded the same as an aftermarket radio harness, so it is simple to know what wire is supposed to hook into what spot on the amp as well as behind the radio.  The nineth wire is for your remote wire to the amp.  it puts every wire you need in a simple, clean, well shielded, easy to run location.  You should be able to buy it at a local car audio shop.