Are you playing cd's or running ipod only? If ipod, check the compression of your files. Make sure they're not 128 kbps. 256 will give you far superior sound. Also, look at the Cobalt 300.2 amp from crutchfield for $80

 

also, please turn off that Loud feature, it does nothing but distort sound by boosting 100 Hz and 12 kHz

and, all speakers have their natural roll off frequency, just because they say they are full range speakers it doesn't mean they are made to handle abusive bass all day long. What they mean by full range is that you don't need seperate tweeters to get the trebles

from your situation, JBL seems to be best route atm JBLs are warm amps, they would tame your tweeters abit

 

Running iPod/iPhone only (Alpine IDA-X305 has no CD player built in) and everything I've ripped from CDs is 320kbps, downloaded music ranges from 128-320kbps.

Also, loudness is definitely off... they helped the stock speakers, but distort the hell out of these Polks.

 

That sounds like a good plan. Keep in mind that if you do get an amp you still can get away with no sub since your mids will be getting a lot more juice. It just won't thump quite as much. Try with an amp and no sub and see what you think...worst case you can stick a 10 inch in the back.