BEST HORN LOUDSPEAKER TO PURCHASE

I finally looked at your JBL 4349's (sorry I didn't look them up earlier)

I think your problem, with them, is they are only 2 way. JBL includes level controls like they used to, however, for the 2 way models, they only alter the tweeter, there is no midrange.

I think you need a 3 way speaker, with level controls for both the midrange and the tweeter.

Normally, you adjust them in your space, to get close to flat frequency response, and finally adjust for your personal preference

For you, listening at low volumes, I think the secret will be to reduce the midrange control (relative to the woofer), so when you get down to (or up to) say 53 db, your 'curve' will automatically have more bass than 'flat'. 

After a few days, then adjust the tweeter, for less or more as per personal taste.

Like their Model 4312G

https://global.jbl.com/on/demandware.static/-/Sites-masterCatalog_Harman/default/dw40b7379d/pdfs/JBL_MODEL_4312G_OWNER'S%20MANUAL_EN.pdf

It has separate controls for the midrange and for the tweeter. Nicely, they are on the front, my AR-2ax are on the back.

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Other makers, vintage or current include midrange level controls which I believe is the solution.

IF/when playing at higher volumes, front controls, then it's easy to turn the mids back up to 'normal'.

Sum it up: cut the mids rather than boost the bass.

I contacted Greg at Volti who confirmed that my 100db Volti Rival can handle 2watt SET amps. Besides its efficiency, I choose Volti for its neutrality so I can explore tube Sonics. 

The O/96 is less efficient, but it’s one of the most musical speakers. Maybe I’ll pick up a pair someday to compare tube amps with my Volti - what fun!

To get a horn bass unit one usually needs a larger room. The Volti Vittora is an example, but is out of budget. Maybe a used Klipsch Bell with Volti upgrades.

I am a long time audiophile and have owned several brands of speakers including Sonus Farber, Harbeth, Omega, Monitor Audio Monitor, Maggies only to finally land a pair of Klipsch Cornwall IV's which I modded per these Forums and finally learned I am a horn guy through and through.  That said, if I were building a second system for a smaller room (my current rig is in a huge room) I would buy a pair of locally built (to me) Shinjitsu Audio speakers.  Check out the website and some on line reviews....they are awesome, especially low volume.

Have fun

I would not make any choice based on theoretical advantages or disadvantages of particular designs.  Big bass drivers in horn systems are out?  Some of the best low volume systems ARE horn systems with gigantic woofers.  I’ve heard dozens of systems with 18” woofers; my own terrific low-level system has twin 12” drivers.  You can find good low-level systems from a wide variety of designs.  The Volti horns, Charney fullrange single driver systems, Devore and Audio Note two-way box speakers are good examples people here have suggested.  The two-way system with multiple tweeter arrays of Tekton are also good at low volume.

At extremely low volume you are not going to get deep and impactful bass.  What you need is something with clean bass down to 50-60 hz and a very good and lively midrange.  This is where most music resides and so upper bass to upper midrange matters the most.  I tend to like horn systems that do well in this range, but, as noted above, other kinds of systems can do the trick too.  My own personal choice for low volume listening would be a good horn systems, Charney Audio Companion fullrange driver system, or Quad 57 electrostatic speakers.  If I were listening only at low volume, I would go with the Quad 57.

By far the best audio demonstration I’ve experienced was Devon’s Art Of Noise in San Francisco. 
 

https://ojas.nyc/products/sun-audio-sv300be-kit?Tubes=Western+Electric+300B+w%2F+WE300B+Tubes&Workshop+%2B%24400=Yes

Right from the needle drop the presentation had that element I so enjoyed from my Marantz 8B’s / Altec A7’s VO the T in my large loft space during the early 60’s. You’re in the groove, good luck with your search.