You budget sucks. Low quality systems sound like rubbish. Have you thought about buying high-end second hand gear?
I have a set (4) of 6inch Schneider speakers, came out of my 140db set up. In good, but used condition. The crossovers show wear and tear on the plastic casings, but you can't see them behind the door.
They were $2k for 4 a few years back. I want $500obo. You will need an amp to power them though.