2007 Mazda 3 Hatch - Upgrade Bose Door Speakers

Sir

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2007 Mazda 3 Grand Touring Hatch
I've been looking around trying to find some information on what to do with my car, but I figure just making a thread would get me the answers I need.
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I've got a 2007 Mazda 3 with the "Premium" Sound System, meaning stock everything.

I plan on installing a 12" P3 w/ a 500w mono-class amp early next year.
This speaker-replacement is just to tide me over.

I was thinking about throwing a pair of Rockford Fosgate 6x8 2-way Speakers in the front doors, but I'm not quite sure if it would be effective.
I've read that the stock amp is about 222 watts, meaning 150 watts to the sub and about 18 watts to each of the door speakers. I don't know if this is true.
For some reason (possibly because the stock sub is beyond s***) I don't seem to get any bass out of my system, aside from what my door speakers put out--which is decent.
I suspect that all of the amp's power is going to the door speakers rather than the sub.

If I go this route, will I need to wire in a new amp?
I'd prefer not to, but seeing as these speakers are 4-ohm and 80 watts RMS, I'm afraid I may need to.
Would it be better to go with lower-RMS, 2-ohm speakers? Or would they run fine off of the stock setup?

Could I get some help on what to do?
 
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