Subwoofer recommendations for this system?

I am in the process of seting up a new system:

Ah! Njoe Tjoeb 4000 CDP with all upgrades
Bottlehead Foreplay preamp
Wright Audio 2A3 monoblocks (3.5 watts)
Reimer McCullough speakers (+/-3db 42 to 20 khz, 94dB efficient)

Room size is 15x20 ft with a cathedral ceiling sloping from 10-18 ft, and opening into a very large and high hallway. I listen to many styles of music, but mostly jazz (both acoustic and electric). This room can quickly become "boomy" with too much volume or too much bass, but the Reimers alone do not provide enough low end.

I am looking for a very musical subwoofer that will fill in the lower octaves, and integrate seamlessly. There is no home theater requirement. Budget is $1000 max.

Thanks in advance
Without ever hearing one myself, the first sub I'd recommend for your application would be the REL Strata III. I think for your power and musical requirements it would be very tough to beat. Hopefully some people that own the Strata III and have a similar rig to yours can offer some real experience.
A few days ago, there was a used Bag End Infrasub 18" subwoofer for $900. It could have been an auction but it was here on AG.

I've had one in my home for about 2 weeks some time ago. Very musical. I had no idea at that time that an 18inch sub could be so well defined and tight in the bass down to an unbelievable 8Hz they say. I do not doubt it.

Stereophile had very good things to say about this subwoofer also.

I stepped down a notch from the sound of the Bag End because I wanted a few more bells and whistles and ended up with a Triad Platinum 18inch subwoofer. The Triad is much like the Bag End, just not quite as tight and will not go down to 8Hz(not many will). You could find a Triad for about $1k used also.

The Bag End is not the best fit'n finish, nor the most easily configurable, nor the most options, but for $1k used, I do not believe there's a sub out there than can hold a candle to the Bag End's performance from a musical perspective.

Easy one. ACI Force. One of the most musical subs you can buy with surprisingly high clean output capability. Having compared directly to REL Strata III and Storm III, the Force was the winner as far as my friends and I determined. Looks very cool as well!
Check this out. I know it's never recommended because it's not really advertised by Sunfire that much. Give a listen to their Architectural Series. It is designed for two channel systems. One front firing 10" or 12" woofer, depending on model. I did tons of research and listening when possible. Spoke to Bob Carver and others. You can find this baby, brand spanking new, nicely discounted. It's fast,very low extension and seamless with my system. I have the Revel M20s and set the sub's x over to handle the lowest end. Does everything a quality sub shoud do. I listen to mostly jazz, but his baby, if you want to show it off, will rattle windows and pictures. I love mine.
Yeah, I forgot about the ACI line of subwoofers like the Force, Titan and Titan II. Many people have compared them favorably to RELs and some of them actually will fit within your budget brand new.
Given the equipment you own, I'd surmise that reproducing the essence of the recorded music is a high priority for you. Hence, think about subwoofers that are noted for their musicality as well as their ability to cleanly reproduce the lower frequencies, and for their ability to integrate seamlessly with the rest of your system.

With those two criteria in mind, the Vandersteen 2Wq subwoofer should definitely be on your short list. Used units often sell here on Audiogon for $800-950.

You might want to do a search of Audiogon's archives to look at the many articles that have been posted about subowoofers, including the summaries of articles about subs taken from a number of audio mags. If you do so, you will note that 4-5 subwoofers consistently rank near the top, with the Vandy 2Wq being one of them.
We have similar rooms and satellite speak efficiencies (Ref 3A de CAPOS- 92 dB). I recently added a SV Sub PC-Plus. I am very happy $750.00. If you go that route, tell them Robert Hart of Audio Tweakers sent you. No commission, just brownie points
Thanks to everyone for your suggestions. I called Rick Reimer (who built my speakers) to ask this same question, and he said he will build a subwoofer for me (tuned to match my speakers and using the same veneers for the cabinet). He does not advertise them on his website, but will custom build them for customers. And, his price was very reasonable!
I would want to know some details about any "custom" sub. Particularly the amplifier that will be used and what the warranty will be. Companies like REL and ACI use custom built, very high quality amplifiers that are extremely reliable. These would not be readily available. Many of the plate amps that are easily available are not particularly reliable or of very good sonic quality to begin with. Make sure you find out details of the amplifier used. I guess it just strikes me as odd that they don't advertise a sub but can just come up with one. It is entirely possible that they have a real good one available, I'd just want to know more specifics of amp- driver- tuning all that good stuff:)
Tiny, you bring up some very good points.

I really spent a fair amount of time researching subs and auditioning them before I finally shelled out money. I found that I simply could not live with most of them. I also asked the various companies a lot of questions. One of my concerns was reliability. After all, if a subwoofer amp fails it can be a bit of a hassle, one I'd rather not have to deal with, or pay for. I've sure heard a lot of horror stories about certain plate amps and even certain models from the "big boys of subs". I just can't quite imagine throwing together a powered sub and having it be able to compete with designs from companies that have invested years into getting it right.
I have my concerns with plate amps as well, that's why I've decided to build a pair of stereo subs and run them off my Bryston 4B.