I say regrettably because I've always felt that subwoofers were an ersatz way of achieving full range sound quality and that a properly designed 2 or 3 way speaker in the appropriate room should provide more than adequate bass.
I think a separate sub is actually a smarter way to get full range sound. When all drivers share the same cabinet, low bass output is at cross purposes with the rest of the speaker's range. The bass waves are so large it is difficult to control cabinet resonances and keep those large backwaves from affecting the excursions of the other drivers. It also is the main reason for increased cabinet size, extensive bracing and higher cost. It also tends to necessitate a bigger front baffle, which compromises imaging and soundstage (there are exceptions of course).
Separate powered subwoofers make speaker placement easier as you can place the primary speakers for best tonal balance, imaging, and soundstage, and then place the sub(s) for flattest and most extended bass response. Powered subs also enable you to adjust volume and phase for best blend and overall response. Just because the single-cabinet full-range speaker came first doesn't mean it's the best overall solution. You may also get cleaner sound because the bass waves are generated from a separate cabinet and are powered by a separate amplifier.
For recommendations, I was really impressed with B&W's PV1D
. I heard it with a pair of their PM1 minis, and the sound was seamlessly integrated. That's a really good sub and list price is $1500 (I think).
You maximum budget would also allow the JL Fathom F110
. Fathoms have a really fast rise time and also integrate well with speakers of all sizes.
I've heard the PV1D with mini-monitors and the Fathom F212 with a pair of Magnepan 20.1s and in both cases the bass was seamlessly integrated with the mains and there was no discontinuity between the subs and the mains in transient response or timbre. They also have excellent extension.