I'll chime in, realize I am biased towards replacing the stock system. If you haven't seen it, here is my build thread on my wife's car.
http://www.zpost.com/forums/showthread.php?t=784148
IMO the best route for the money is rip and replace, you get new technology, and way better sound. New speakers, and an AMP and you will be amazed at the sound.
If you want to preserve the stock head unit then you will need a sound processor to convert the speaker signals into a signal usable by an amp. You mention JL, this is a sample of what they have:
http://www.jlaudio.com/car-audio-oem-interface
You will still have the cost of the new speakers, and new amp, and the signal processor(s) will cost more than a new head unit. You don't get new technology features such as blue tooth streaming, etc...
Upgrading the speakers only would be my last choice, as others have mentioned, you have the issues of impedance matching, and the improvements are marginal for the dollars spent.