The Best of the English Sound

Given your setup I'd suggest a good subwoofer might be another angle to pursue/consider.

At the lower end , the Wharfedales are amazing. You could step up a bit to the Audioengine A5s that are powered.
ATCs need a lot of power.
The Harbeths and Spendors are the next step up and need less power. They are both less strident than the ATCs. Not English but the Reference 3As may fit the bill.

You mention that you are using cheapo Behringer amps? I think that is possibly the main problem that needs to be addressed before you even considered changing speakers. You can't get a good sound with cheap amps, at least I never have been able to. I'd look for a nice sounding amp for the money you are willing to spend and then see how you like your speakers.

Ejlif

Thanks and I have thought about that, but if you search other threads, you will see that the cheapo Behringer A500 is supposed to be a "giant killer."

I am using two of them as monoblocks and biamping, where they barely break a sweat as I use them mostly for background and TV.

This is not to say that they truly are giant killers, or suggest that a Pass or Levinson or LAMM or ARC wouldn't sound better, but under the circumstances, I thought the amps were the least likely source of an edge in the system, and that even with those components, the differences between ATC, Spendor and Harbeth would be clearly audible.