Does this speaker exist?

Drubin,
Yes! A practically countless number of speakers fit your criteria, optimum set-up and placement is essential so the loudspeakers interact (mate and play) with your room.
Please purchase Jim Smith "Get Better Sound" I recommend the Book and DVD, a wealth of knowledge for cheap.
Even a $30K pair of speakers can sound "not correct" and even "bad" if not set-up for optimum room placement (almost sold mine), a well designed inexpensive pair can sound magical, musical, correct and Great! leaving you not wanting for more (I have done this with a $500.00 pair).
Please do yourself a favor: get the book and DVD.
Jim C. PS: Before you spend a lot of $$$.

Dan, Yes, it exists in your dreams. Tired of the Dunlavys? I'm thinking about getting back into Dunlavy SCIV, but my back hurts everytime I think about it. I have always wondered how the SCIII compares.

I'm ready to sell the Dunlavys, let me know if you want to have a conversation about it.

Zenblaster -- I have a pair of the LS50. I don't think they're quite what I'm after, but maybe, as Jimc555 says, it's a setup problem.

Drubin - you just described the Thiel sound! Will not fit your under 40" height though.

For Rrog above, I had the SCIII many years ago at home, and used to sell Dunlavy back in the day - the 'III is missing the bass foundation that the 'IV has in spades...actually, except for being too tall, the 'III meets the OP's criteria right down the line.

But I doubt you'd find them satisfying, having grown accustomed to the more full-range sound of the 'IV.