If the OP´s problem has to do with unexpectedly dominant reflections in the new room, an EQ or automatic room correction systems like Dirac are the last things that will sort out anything. EQs are meant to correct for solely tonal imbalances, they cannot counter reflection issues coming in later or from a different angle.
You do not need different speakers, you need to place them differently.
If overly dominant reflections/reverb at the listening position is the issue - as the OP has hinted describing the room as ´reflective´ - the only positioning strategy that really helps is a radical nearfield setup. I don't know if anyone wants to sit as close as 1.2m (4ft) to the speakers, but that is a typical average critical listening distance in a reflective room.
If one does not want that, well different speakers seem like the only option.
Rodger West's Sound Lab Electrostatics have a super narrow dispersion.
From acoustic point of view, narrow dispersion panel speakers seem like a good idea in a reverberant room. As the OP described the situation, there are several seats, so speakers with an overly narrow horizontal listening window sound a bit problematic to me, as they cannot cover several listening positions.
The only viable solution here would be speakers resembling a line source, but except from Perlisten, there are not many manufacturers in this price range.