Need Advice on Subwoofer Selection

I recommend REL sub, hi-level connection obviously. I used Velodyne sub but was not happy with it in stereo, great for HT though. I had quality issue with it also. Rel is more musical, probably one of the most "music friendly" subs, easy to integrate with a system.
Your Proac 2.5 or 38 would benefit from a sub as well. Sub in a system is not only deeper, tighter bass but improved soundstage, more open, more "air", more micro detail.
You have to set the crossover properly, most people set it to high.

You can buy a pair of Gallo TR1D's for 1200.00. They have a small foot print and a small face profile since they are round. They are super easy to set up and just plain kill my previous REL sub.
I'm using speaker level inputs and run my mains full range. The TR1D produce bass when called for and never sound heavy or slow. They will follow a bass line like a bloodhound.

I'm using a pair of MJ Acoustics ref200 with synergistic ref speakon and subwoofer rca cables with WB Arcs with very good results. It also has a remote control with four presets which simplifies adjustments when needed. You can also use the speakon high level and low level rca simultaneously for better tuning as each has its own crossover and volume setting.

Give a Ken Kresiel DXD808 a listen, it has the foot print your looking for and at under 2K, it has dual 8" drivers in push pull configuration with 375 watt mono blocks for each speaker and extension down to 10hz. I own its bigger brother the DXD12012 and its the accurate lowest distortion sub I've heard and the reviews say the same.

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.