Please Recommend Highly Efficient Floor Standing Non-Horn Speaker Suggestions

Among my favorites are Charney Audio Companion (Particularly with AER driver option), Cube Audio Nenuphar Basis, Fyne Audio F1, Audio Note AN-E..

If you are willing to do the audition at home and return if not satisfied routine, you should audition the Tekton Double Impacts.  In their price range they are pretty good--reasonably full and rich as well as being clear and detailed.  I personally don;t care that much about how something looks, so I did not mind that fit and finish is not in the class of the very best speakers.  Near that same $3,000 price range, and also quite efficient are the Rethm Bhaava (has powered woofers, amp built in).  

we might need a definition of horn here.  Are we talking about a system with a midrange compression driver, or do all of the drivers have to be horn-loaded?  Does a woofer with a front waveguide qualify as a horn system?  What about systems that have a quarter wave backloaded horn structure?

I like a lot of systems with old school vintage midrange compression drivers--Western Electric, International Projector Company, YL, etc. drivers, and a small handful of modern replica drivers (mainly G.I.P. Laboratories replicas).  These systems may or may not have compression tweeters and woofers can be of all sorts and in all kinds of enclosures--open baffle, sealed enclosures, infinite baffle (particularly like Onken versions), or horn-loaded bass cabinets.

But, I don't think that good high efficiency systems necessarily have to use compression drivers.  I've heard a number of systems using full-range dynamic drivers in either single-way or multi-way systems that are terrific sounding.  Whether some of these are also categorically horn systems depend on how one defines horn (e.g., Charney single-way systems use quarter wave back loaded horn cabinets).  

The fact that OP asked about non-horn systems suggest a dislike for "horns."  I suspect that this is the result of hearing some more common horn systems that were not to that person's liking.  This is a bit regrettable because there is a vast array of horn systems with quite different sounds, including many that don't have a peaky midrange or tendency toward a nasal coloration that one often hears in more common horn systems.