Research for subwoofer

Which is which? Sub-Bass Systems was the term Richard Edmund Lord the R.E.L. of REL used for his systems.  

REL subwoofers (I still like our original term Sub Bass System for its more complete description of what we do) 

This admonition was from a website brochure by the current owners some time ago. Another consideration, the company matches their systems to a list of speakers.

-3dB subwoofers are positioned and adjusted to integrate with most any speaker and room. Update your speakers and simply readjust your subwoofer.

Despite these differences adding a sub-bass woofer system offers setup simplicity and a reasonably enjoyable presentation at the expense of the surprisingly stunning extra low frequency found on many recordings and programing. All the best with your search.  

Given the volume of your space and bookshelf speakers a stereo pair of subs would provide a major improvement.  If you're focused on 2-channel only REL would certainly be my first choice.  They really integrate well, when setup properly you can't tell the subs are there until you switch them off.

@gkelly 

While two subs are better than one, the best way to go is 4 subs for a distributed bass array. If that is not possible, two subs gets you most of the way there.

@tcutter so what is your opinion about a REL6 pack line array or were you thinking duel six pack line arrays? Bet that would kick butt! Definitely OP needs to worry about stuff like this over his budget speakers with his $10,000 amplifier.

@gkelly valid observation on speaker pairing ...

Many good SW reviews here:

https://www.audioholics.com/subwoofer-reviews