That's a very large room. In my opinion, speakers that have a good dynamic capability and smooth power response with robust bass tend to be good candidates for a very large room (think "prosound-style but with smoothness and deep bass"). One way to get smooth power response is to use a big constant-directivity horn and a big woofer, and to cross over where the woofer's pattern has narrowed to match the horn's.
Have you considered something like the Altec Model 19? Long since out of production, the Model 19 is a high-output classic with very good bass and smooth power response.
Seldom available used, but within your price range new, the PiSpeakers 4Pi embraces essentially the same design principles as the Altecs mentioned above, but with more modern, higher-output drivers and an even better crossover. The designer, Wayne Parham, is a master. If you go for the 4Pi, get the JBL woofer and B&C tweeter upgrade, both of which are well within your budget.
Duke
dealer/manufacturer