Your room size is similar to mine with hardwood and openings to other rooms. I have not heard a wide range of speakers, but my research led me to Fritz Speakers. I chose the Fritz Carbon 7 SE Mk II. At $2500, they are on the lower end of your budget, but I also paired them with a Rythmik Audio F12SE Subwoofer to fully round out the frequency range.
I have been very pleased.
Good luck!