On an ap1, press harder on the right pedal. Even
Though our gut tells us it's the wrong thing to do.

 

So I finally got the issue resolved.

Here's what I did that didn't help:
changed rear diff fluid at a Honda dealership
Swapped stock suspension for KWv3's
Got car aligned and corner balanced (this helped a little bit, but not a lot)
Installed volk RE30's with Hankook RS-3 tires (to replace terrible tires that the dealer put on the car before it was sold to me.)

After that was all done, the car still pushed wide with light power and light cornering. The shop said that the sway-bars had preload on them after the corner balance and I'd need adjustable end-links to fix that. So I ordered them.

Here's what I did that fixed it:
I had the alignment shop put on the adjustable end-links and adjust them properly.

The car is no longer swerving all over the place when I apply throttle around a long bend on the freeway. It was so bad it would almost change lanes for me.

I have no idea why my car exhibited this behavior when it was stock as I would assume there would be no preload on the stock sway-bars with the stock dampers and springs. All I know is that it's fixed now AND THIS CAR'S HANDLING IS GLORIOUS.

 

You don't need adjustable end links to remove preload from a sway bar, they just have to be installed with the suspension loaded.

 

Congrats on the fix....sounds like you have some top quality components! Enjoy your glorious handling!