At 7200 ft3, you are well beyond the ability of most home speakers to effectively fill the space. There is only so much output a 1" dome can put out into that space. Additionally, you do NOT want wide dispersion in that large of a space, too many reflections, or if you treat for them, not enough output.
You are in the realm where horns will simply be a better fit, work better acoustically, and be more satisfying. If there are two symmetrical corners on a short wall, then K-Horns may be an option. Cornwalls are bass limited to roughly what a smaller bookshelf can provide, just louder. They need a subwoofer, which is off-limits in your requirements. Both recommended with numerous caveats and mitigations required.
Next up, JBL 4367. They would have no problem filling this space, have proper dispersion for large spaces, sound wonderful, have the low bass the Klipsch lack. The only issue would be the cost - new, they are $16,500 a pair. And worth every dime. There are a couple pair on eBay right now in the $11-12K range. Highly recommended.
An interesting option would be the JBL 3732T. These are for-real cinema speakers, and would require building grilles for most domestic use to achieve any level of acceptable WAF. Cost wise, they are in budget at about $8000/pr. However, they require triamplification (1 - 2ch 100-200 w/ch bass, 2 - 2ch 50-100w/ch mids and highs) and a 3-way electronic crossover (2- DBX 223s recommended) plus cabling, plus a DIRAC-enabled front end, plus install and tuning. But, the end product would be stunning.
Big Magnepans, maybe, but with big power only. And without seeing the rrom, it's hard to tell if Maggies (full disclosure, I love Maggies, big or small IF they're set up properly in an appropriate room with appropriate power)
There are other horn speakers that may work here, but I'm not familiar enough with them to make a recommendation. But again, this space is just too big for direct radiators to handle. It's just a physical limitation, and acoustics is just applied physics.