Speakers least affected by room acoustics

Something very directional like Magnepans would decrease the echo but they have a smaller sweet spot.  Any conventional box speaker will have the echo.  Something with a small midrange will have more even dispersion so the echo should be less objectionable.

Don’t compromise.  Look up Vicoustic Flat Panel and Cinema Round absorption products.  Gorgeous looking and very effective.  Oh, and relatively inexpensive for the performance benefit you get not only for sound, but as a living space as well.  If your room is that bad, I guarantee the panels will maks the room more relaxing and less stressful to be in, even if on subconscious level

Using the Cinema Round 2x2 panels in an arrangement like they show on the web site looks like high end wall art in person.  Keep in mind, the images they show on the site have dorky lights behind them.  Having them flush with the wall looks much better.

A heavy rug on the floor would work wonders

I don't think there is a speaker on this planet that is not affected by room acoustics in some fashion.

Sounds like a problem at higher frequencies. Apart from listening in near field, there is only one solution and that is to dampen the reflections.