In all honesty, the stock Lexicon speakers in the Genesis are as good(if not better) as most
aftermarket door speakers in the sub $200 dollar price range. The pricier speakers will need a stronger amp to sound better as well I believe.
However, you could just use a very high quality high-level signal convertor that can handle 100watt rms outputs and then spice into the speaker leads exiting the lexicon amp to provide a signal to the
aftermarket amp and then splice into the wires going to the door speakers for the sound exiting the
aftermarket amp speaker output. I am doing that to power my
aftermarket subwoofer amp for my Kicker sub by tapping into the stock amp subwoofer output.
I am surprised the Audio Shop did not recommend that option to install your 5 channel amp. However, they probably did not want to splice the Lexicon amp wiring ;especially if they do not have a proper wiring diagram for the Genesis audio system.
Note: You may have to install some load resistors(2 or 4ohm) on the stock amp speaker output leads feeding into the signal converter if the signal convertor do not create enough load resistance so that the stock amp will not go into protection mode if you remove it directly from all the speakers. I installed my signal convertor in-line with the stock subwoofer still connected, so my stock amp still reads a load and works just fine.