Forgive me for coming across as a little slow, but....
Is it fair to say that since the speakers are rated at a LOT more power than the stereo unit is making, the speakers are just not getting enough power? Would one solution be to switch to a lower rated speaker OR should I rig in some type of amplifier?
Kern, you are not slow if you are driving that Charger! Just remember that!
As for the speakers, I think you would probably be better off, if you are OK with it, installing a smaller 4 channel amplifier to drive your speakers. You don't need anything huge. Something in the 45-75watt RMS range should be good.
Most will probably be around 50 watt RMS. This is just a consistent rating, all amps will have also have a peak power rating, meaning that on heavy notes, or turned up, they will produce a lot more wattage for short periods of time, so do let it fool you that your speakers are rated 120 watt RMS, but you would only be using a 50-75 watt RMS amp. It should still be more than enough to do what you want to do.
From the specs and the reviews I read, your speakers are pretty good and you would really be downgrading to try to find ones that would work using the head unit for power alone. Your head unit is good as well, and can be tweaked by the right person to help dial it in with the amp to sound really good.
If you try to power speakers from your head unit alone, it will never sound as good, loud, or as much bass as your Ram, (not even close) even with matching more efficient speakers to the head unit. I think if you bought new speakers you'd just be disappointed again and end up wasting money. A small 4 channel amp would be money better spent.
You could probably get one with the wiring kit for $150-175ish to $250-275ish depending on brand and your budget. I would look at Kenwood, Alpine, JL Audio, Memphis Audio, Rockford Fosgate, JBL Audio, Pioneer, or Kicker. They should all be around that price range and will be able to do what you want.
I would also say that with a smaller 4 channel amp and the size of your speakers you should most likely not have to do anything to your electrical system. If you add a subwoofer at any point to the mix you would most likely need to do something.
I would suggest, having worked at them, go to an actual auto audio store, skip the big box stores like Best Buy, and tell them what you want to do (a basic 4 channel amp to boost your output some), and see what they have. The stereo store will be able to better elaborate on the differences and/or advantages of one brand over the other, and maybe have something on sale.
Again, I would avoid anything with crazy power ratings (like 250 watts rms / 2000 watts peak), all the cheap brands, as they will all sound like crap, or burn up; like Zues, Hifonics, Dual, Boss, Autotek, Pyle, Pyramid, Lanzar, or Planet Audio. If you go somewhere and that is what they are pushing, walk right out.
Hope this helps. Paul