Box speakers that sound like Electrostats?

To answer your question Dennis, no. But there are some that offer the better attributes of stats. To the ones mentioned I would add the Merlin VSM-M. It is a 2-way is quick as lightning on transients, holds on to a note, decays to infinity and is tonally evenhanded like the better stats. Add to the above, world class resolution and an ability to retrieve the subtlest details of the recording providing you have the right gear in front of it.

I've only heard one stat I could live with if I had the room and the money. Most have too many compromises that offset their virtues.

As much as I hate to admit it regardless of the hype Muralman1 is correct. No box speaker I've heard can truly escape the box and completely disappear as a well set-up dipole can. The Merlins are in the top tier so far as disappearing goes. On the other hand unless the system is large enough most stats compromise on the macro dynamics of music that bring it to life. I can live with a little boxiness rather than limitations on dynamics, a personal preference but others may demur.

This can be achieved with stats but it takes a large diaphram and room for starters. The other problem is bass performance. If you want great bass and a stat, subwoofers are out for me. Gotta have the large panels pushing the bass. The coherence is lost with a subwoofer. It may not be apparent at first but it will catch up with you sooner or later. Dipoles are about speed and refinement. A dynamic driver thrown into the mix just can't keep up with the speed of those panels. Choose your poison, nothing's perfect.