I'm hoping to avoid having to run new wire to each and every speaker but I'm running out of ideas. I started out with:

A 2007, grand prix base, no monsoon system, factory original head, and I believe the factory speakers, a set of 6.5's in the door, 6x9s in the trunk deck, all paper coned. I experienced a faint amount of distortion in the system at high volume but it wasn't horrible, I only decided to try and lose it because of my tax refund allowing for an upgrade.

the new system consist of the following: a pioneer dmh-bt160 head unit, ran through a metra WM-gm11-swc adapter to retain factory steering wheel controls and chimes, and schoche 200 watt 6.5-6.75 speakers in the front door panels, schoche 300w 6x9's in the rear deck connected using Metra 72-4568 speaker harness adapters in the hopes to keep a plug and play system.

I used to get a bit of alternator whine so I plan to check the grounds once i figure out where they are, but I wanted to ask for help on what could be causing the distortion so I can cover it all in one tear down (hazards of it being my daily driver, I have to put it back together well enough to keep using at the end of the night).

I'm also aware of a couple other odd things, everything I've seen says the 07 grand prix has a factory amp but it was absent from the trunk, and I know I'm under powering the speakers but I was under the impression that would just mean i'm not getting as much oomph as i could possibly squeeze out of them, as the pioneer head provides 50 watt x 4 channel.

I apologize in advance if any of this is obvious ignorance, I've only done once with slightly better results previously.