low frequency extension adding a sub makes sense. I would look at subwoofers that are sealed, servo controlled, and exhibit low Q. Unfortunately, you probably cannot get that for less than $800, unless you buy used. That said, you could do a lot worse than an Epik Legend for $500 to go with Martin Logan Motion 12s. If you can spend a little more, the SVS SB12-NSD at $650 would be good also. Ultimately, the Rythmik subwoofers are probably one of the best for music under $1000.

I am not concerned with the sub being sealed than with it incorporating decent EQ to compensate for room modes.  That, imho, is the major influence on in-room performance.