Are there speakers like this?

Three way design.
LF driver TL loaded or in compression enclosure (not any flavor of Bass Reflex).
MF driver not made of Kevlar, carbon/glass fiber, rather fabric soft dome, or some sort of polymer, etc., that is wide dispersion.
HF driver not made of any kind of metal, rather silk soft dome or similar, that is wide dispersion.
Or alternatively, some omnipolar design with such MF/HF drivers configuration and LF drivers in TL or compression enclosure.
And MSRP is not above 8K.
Candidates that almost meet criteria are for example PMC OB-1 (but they are not dispersive enough), or Mirage OMD-28 (but they are Bass Reflex).
A 3-way?

You can find more of what you want in certain 2-ways.

You may discover that drivers with a vented pole piece do not sound like typical "bass reflex" designs.

Since few "manufacturers" build their own drivers- focus on the brands of drivers themselves. In the end, you may need to assemble your own speakers from drivers that meet your criteria.
Not lately.

The last 2 requirements are easy to find but acoustic suspension and trans-line seemed to go the way of the dinosaurs. Too bad.

How about some old Dunlavys?
Sounds like the AR 3a.
ATC speakers fit your bill exactly - second hand you may find a 50 or 100 close to your price. Much more dispersive than most other speakers (soft dome tweeter, 3" soft dome mid range).

I assume you don't want a reflex port because you worry that it will sound boomy below the port tuning or "chuff" with air movement at high levels. No worries....ATC's reflex port is NOT at all tuned to augment bass extension as in almost all other designs. The reflex port is tuned to control/protect driver at ultra LF and allows the use of a more efficient driver for high SPL and greater dynamic range.

If it is an aesthetic thing that you don't want a reflex port then the smaller ATC models don't have them (SCM 40 and lower)
Read this. Linkwitz Orions

Maybe it will meet your requirements.

Disclaimer: I am an owner
ADS L710 or L810
Why not go custom? Since you know what you want have someone build it for you.
classic AR's , ADS, DUNVAY, HALES,DUNTECH....not entirely there, but cop outs in their designs
check out chapman audio. his t-7 or t-77 might fit your requirements. there are several threads on audiogon.
Thank you all for suggestions, looks like I will be on a quest to locate suggested ones for listening, if possible.
Shadorne, the reason I do not want reflex is not aesthetic, but sonic.
Just yesterday I listened to Mirage OMD-28, very nice performer, but there was something that bothered me enormously in LF/LF-MF range, not so much boomy, it just lasts too long and produces something that masks otherwise clear midrange (I guess it was chuffing).
What I want in acoustic drums reproduction is to hear clear and fast thwack and nothing more, there is no any kind of “decay” when you listen to live drums.
I am not terrible demanding otherwise, but it is hard to find speakers that can reproduce proper LF foundation for music.
I am yet to hear reflex design that I like (aside Gershman Black Swans which were very impressive at first and which I did not listen to carefully since they were out of my price range).
Good to know about ATC, I was thinking about them, but was put off by reflex design.

Question on dispersion and 3D soundstage formation. Let’s say I go with PMC OB-1. Am I correct to say that I could get decent depth and height of the soundstage with relatively low dispersion speakers if I give them enough room, place them let’s say 4-5 feet from the back wall and listen 9 feet or more away, to allow proper combination of direct and reflected sound to reach my ears?

Johnk, custom or DIY is a lottery. No way I can get everything right, match drivers, have proper cross-over, I simply have no enough expertise and no tools.
A friend of mine who has very similar taste in terms of expectations from speakers has tried DIY project, and while it was very good job, ultimately it did not meet the expectations.
Is this similar to what you seek Music& Design Nao speaker system?
Acoustic suspension drivers seemed to favor speakers that utilized a horn/compression driver combo. They rock- if done properly. I'm thinking Altec did it best- early Altec. Why not consider a classic 2way like a pair of Model 19's? When you rebuild the cabinets and crossovers- you really have something. Midrange galore and none of the bass reflex type artifacts. Since you are particular about the materials in the HF- a well damped horn (811B) with its voice coil in-line with the transducers'- you eliminate the loading. Not that I think my advice will be followed but- They are well worth the effort. Gotta be rebuilt to be up to snuff, though.

The ADS 710s and 810s were GREAT speakers, hard to find a good-condition used pair...