Yeah, honestly, in your room size and with your budget, the HSU VTF-2 MK4 is about the only sub that makes sense. It does not have the super small size, but that's just the way it's going to be. There's no magic when it comes to bass reproduction. You can't cheat physics
In terms of bass quality, there's no better choice available than the VTF-2 MK4 for $500-$600. HSU has the VTF-2 MK4 on sale right now, so after shipping, it comes to $582.
If your wife simply will not have a sub the size of the VTF-2 MK4, I'm not sure what to tell you. You could aim for the SVSound SB12-NSD at $649, shipping included. But it's honestly not meant for that sort of room size. You can check out Audioholics' review of the SB12-NSD to get an idea.
Physically small subs are going to be sealed. That means 100% of their output has to come from the driver, which means that driver has to move in and out like crazy, and or be a very large driver, in order to play loud enough to fill your volume of air.
I'm no fan of the Def Tech SuperCube subs. They use passive radiators, which is somewhat similar to using a port. But in the case of the SuperCubes, all they're designed to do is to play louder. They give up a lot of quality, IMO, in order to just play louder.
So yeah, if you can make the larger size of the HSU VTF-2 MK4 work for you, that's definitely the way to go, IMO. You can actually put it right beside your couch and have it function as a nice end table. And it's a perfect fit for the Auralex GRAMMA decoupling riser, which you will definitely want on that tile floor!
Speaking of which, you're going to be in some desperate need of acoustic treatments in that room. For certain, get yourself a rug - as thick as you can - to place on the bare floor in between the front speakers and your seating area. Other acoustic treatments will have to come later. Since it is a living room, the "printed art" panels from the likes of GiK Acoustics or Acoustimac are likely going to be the best way to "hide" your acoustic treatments as decoration on the walls. You can have literally any image you like printed on the panels, so they can easily double as the photos, posters or works of art that you would have hung as decoration anyway