Would a car subwoofer work or should I get a powered sub?

I'm looking to get a powered sub for my bedroom setup. I have a 12" Klipsch Synergy sub that sounds great but is simply too big for my room, and I'm looking to get something smaller.

I have a QSC Model 1400 amplifier that pushes 200w per channel or 600w in bridge mono (8 ohms). I have a cable that I can run from the subwoofer pre-out on the back of my receiver into the QSC amplifier (the crossover level can be adjusted from the receiver).

I was thinking of picking up a cheap car subwoofer in a ported box that I can use, or to save some energy and make things easier, I can just find a powered sub. My biggest issue is that most subwoofers within my price range (up to $150 or so) don't really perform well with lower frequencies, whereas if I used a car sub, it will most likely drop down nice and low and I would be using an amplifier that would just be collecting dust otherwise. As an added bonus, I could have two subs with 200w per channel or one sub with 600w.

What do you think I should do?