Rick - the tried and tested method is almost that, but use components instead of coax
changing the front speakers and the head unit is the easiest way to improve the whole sound of the car, you mention quality, this will never be achieved using 6x9s for many many reasons, but lets not go into that
the headunit you have is not exactly a great one for SQ, as with most sony ICE its all flashy lights and gimmicks, and not enough concentration on the quality of the sound
almost every SQ class car has the same theme, decent HU (invariably Pioneer, Alpine or Nakamichi), stereo amp powering front components and monoblock amp powering a single 10"/12"/13" sub (no 6x9s in sight)
front speakers, buy the best you can afford, after all this is what you will be listening to
rear speakers are not neccessary in a car unless you want to give your passengers a little more treble