You have a nice budget, and you are going to need it because that is a very large space. The good news is you only have to worry about one listening position, and that makes matters simple. The subwoofers I would consider in your criteria are the aforementioned Hsu ULS-15 pair, a pair of Rythmik F15HP
, or one of the subs from Seaton Sound
. You have a nice open space right next to your reclining chair, and one thing you can do to get a nice punchy feeling is near-field placement, which is placing a sub very close to your listening position like an endtable in your situation. You might be able to save some money and get a decent sub for that placement, one I can recommend for that role is the Hsu VTF3 mk4
. Place it so that side-firing woofer is blasting right into your seat, and you may get what you are looking for and save some money at the same time.