Does such a speaker exist?

Sorry gents, that was my bad. Clearly the mid 30 Hz range speaker is not a full range speaker... plenty of choices offered, I will offer another speaker...and it is a full range speaker, the Salk SS8.

Ebm,
Are you building a pair of the PBN speakers?

http://jtrspeakers.com/home-audio/noesis-210rt/

These speakers have been at the latest RMAF show and blew many away. Though their stated measurement has bass to 38z, at the show they were flat down to 20 hz. They can do 130db without dynamic compression.

I think Duke (as usual) makes an excellent point. The OP mentioned that he's heard speakers that meet his needs, with the exception of low bass performance. Duke (correctly) notes that low bass performance is - in the world of full/extended range high-end loudspeakers - as much a function of room as it is of speaker. So subwoofers, which offer placement flexibility to suit the room, might be the right answer for the OP.

Duke's four box Swarm subwoofer may be the most flexible solution on the market, but a pair of carefully set-up quality subwoofers will also do wonders in most rooms.

BTW, low 30hz is effectively full-range for music use, IMO. Of the +/- 1500 LPs and app 5000 CDs that I own, maybe a handful ever hit 30hz. Only one (an SACD of a pipe organ performance) has dipped (barely) below 25hz on my RTA (which I leave running full-time these days, partly for this reason). Conversely, the Audyssey set-up sweeps always hit 16 or 20 hz (depending on where I set set my filter) with full out-put at the 75hz set-up level.

I haven't listened to all 6500 ish recordings with the RTA, nor have I stared at it continuously with all the records I have listened to with the RTA engaged. However, I have a pretty large sample under my belt at this point. There may be low level output below 30hz (which wouldn't register on my RTA), but a speaker that offers full range output at 30hz is going to to offer some meaningful output an octave down from there, and that should be more than equate for the task at hand. On that basis, I'd argue that full response in the low 30hz range is effectively full range for 99%+ of available recordings.

Thank you very much, Martykl.

I have Swarm customers who have found that their near-total placement flexibility makes the four small subs easier to accommodate into a living room than one or two larger subs, but that will of course depend on the specific situation.

I've found that even a little bit of distribution of bass sources within the room, such as having rear-facing ports at a different height from the front-firing woofer, plus the ability to adjust the tuning frequency, can add up to a worthwhile improvement. I recall delivering a pair of speakers to a customer who was replacing a very well-respected (and twice the price) pair of transmission-line speakers. I was apprehensive that this would be a very tough act to follow in the bass region. The listening room was modest in size and almost square, maybe 13 by 14 feet. I took that into account when choosing port length, and we set the speakers in the same place his transmission lines had been. One of the first things the customer remarked on when we first fired up the system was how much smoother and more natural-sounding the bass was with my rear-ported reflex box! Who'd a thunk it??

Point being, taking room interaction into account is beneficial particularly in the bass region, even if something like the Swarm isn't practical.

Duke