Omni speakers have been mentioned several times, and there is definitely something they do right which contributes to dealing with terrible rooms: Their off-axis response has the same spectral balance as their on-axis response. Thus their reverberant sound is virtually identical to their direct sound, modifed by the room’s acoustics of course.
Now I’m going to make a claim that will probably be somewhat controversial: In MANY cases, "terrible room" is actually a speaker design issue, but it gets blamed on the room! You see, if the room was the root cause of the problem, omnis would be the WORST speakers for such rooms because they send the most energy out into the room for the room to screw up. But here in this thread we have many people who are experienced with omnis and quasi-omnis telling us the exact opposite!
What many speaker do WRONG over most of the spectrum, relative to omnis (and quasi-omnis like the Shaninians and Larsens and many dipoles) is, their off-axis response is significantly dissimilar to their on-axis response. When the ["terrible"] room reflects back a lot this spectrally incorrect off-axis energy, what we perceive is a weighted average of the direct and reverberant sound, and we make the mistake of blaming it all on the room.
(Now there definitely are room problems which clearly exist, such as too much or too little boundary reinforcement, strong bass modes, excessive asymmetry, too much or too little damping, slap-echo, and insufficient size. Speaker design can only go so far in addressing these issues.)
The fact that omnis sound good in many "terrible" rooms is imo proof that, in THOSE rooms anyway, the issue was not the room itself.
A thought experiment comes to mind: How would an unamplified acoustic guitar sound in the room? If it would suck (like due to excess slap-echo), then the room really is terrible. But if it would sound good, then the room may not be the root problem.
Based on my own experiments omnidirectional is not my radiation pattern of choice because I have concluded that less off-axis energy is actually preferable. That being said, the success of omnis (particularly in "terrible" rooms) clearly tells us what the spectral balance of the off-axis energy should be: The same as the on-axis energy.
Duke