Corner horns like Klipsch! I can't thing of any other type of speaker to sound right under those conditions, irrespective of port position.
The problem isn't port location, as demonstrated by the Audio Notes that Philjolet referred to. Rather, the problem is that most speakers are not tuned (or capable of being tuned) for placement in a corner.
But it sounds like only one of your speakers will be in the corner, presumably the other will be on one of the same walls but rather far from the other corner. So the ideal might even be different tunings for each speaker!
I have a customer who has one speaker in a corner, and the other is next to an entryway that opens into a spacious foyer. His speakers have user-adjustable port tuning, and he has them each tuned for their respective locations. It's an unorthodox but effective solution to an unorthodox situation. Remember, south of 100 Hz or so, you cannot perceptually separate the woofer from the room because the room's effects are indelibly stamped in the woofer's output by the time you hear it. So in the bass region, consider speaker + room to be an inseparable system, wherein the goal is synergy. Again, the Audio Note approach is a beautiful example.
Your room size in and of itself presents other challenges, which imo call for particular attention to the radiation pattern because the reverberant field (made up primarily of off-axis energy) will dominate the perceived tonal balance at most listening locations within the room (nearfield being the only exception).
You might look at PiSpeakers, they are not well known but are extremely well engineered, and will work well in large rooms and with unorthodox speaker placement constraints. Ask designer Wayne Parham which model he'd recommend for your situation. Wayne was one of my teachers and his work is superb. He takes boundary reinforcement into account, and he takes the reverberant field into account. You can think of PiSpeakers as a high-end alternative to Klipsch, without having an uber high-end price tag.
Best of luck in your quest.
I have tried so many speakers since the original Allisons, designed to be placed against the rear wall and the ones that work best are North Creek Kitty Kat Revelators. They are designed specially for rear wall placemat and they will fill your room, even tho they are monitors. Call Rob at northcreekmusic.com and talk to him. They make a floor stander, too. I don't know about the corner, tho, which is why you should ask the designer.
They sound great and probably don't need a sub.
I gave no connection with this company, btw.