$2000 will just cover the cost of the most unique, transparent, unboomy sub of which I am aware: The GR Research/Rythmik Audio OB/Dipole Sub. The catch is that it is not a ready-to-play, factory-finished product. But it's pretty easy to do, if one is sufficiently motivated.
1- You buy the DIY kit from GR Research or Rythmik Audio, the co-designers of the sub. It contains four 12" woofers (a pair for each of two subs) optimized for Open Baffle use by Danny Richie of GR, and a pair of Rythmik's dedicated plate amps (one for each sub, of course) featuring Servo-Feedback control of the woofers, along with a shelving circuit to compensate for the acoustic roll-off endemic to dipole designs. The Rythmik amp also features outstanding controls including adjustable cross-overs (frequencies and slopes), three levels of damping, 1-band PEQ, and, most importantly, a continuously-variable phase control (absolutely mandatory for integrating a sub with speakers. Do NOT buy a sub without it!). The kit is about $1500 including shipping.
2- You buy a pair of Open Baffle H-Frame flat packs from a woodworker who offers them on the GR Research AudioCircle Forum for around $500. Don't worry---I bought from him, he's very honest and trustworthy. The frames are sent unassembled, but are as easy to build as an Ikea bookcase (well, almost). Made of 1.5" MDF (!), they are a truly excellent design, and very non-resonant (unlike the W-frame design of Linkwitz). You then simply paint or veneer the frames to suit your taste and style. See the thread about them on the Forum for details. If this sounds like more than you want to deal with, you could have a cabinet shop assemble and finish them for you.
There was an OB/Dipole sub offered by Gradient in the 80's, for use with the Quad 63 ESL's (reviewed by REG in TAS). This is similar in concept, but much more advanced in execution. Higher quality drivers, with Direct Servo-Feedback (patented by Brian Ding of Rythmik) control of their motion. State of The Art in subwoofers!