From what I was able to decipher out of your post, it's a amp issue. Your headunit puts out about 22 watts of RMS power, on a good day.

Going from sloppy HU power to clean, dedicated amplifier power will be a big difference. I noticed it right away.

Those speakers are most likely rated at 100-125 watts peak, not RMS. Peak or Max power means nothing, you'll never see it.

As far as that Kenwood powered setup goes, it served its purpose in my vehicle for quite some time. And yes, the amp is built into the side of the enclosure. No need for a seperate amp for that.