Balboa mist would be my suggestion - horizon is not modern, and will appear gray white / dirty white . . don't know cornforth but I don't think you want white. . . mist will contrast with your trim ...

I've tried all 3 of theses colours (and many more) on sample boards trying to find just the right gray. My room is also south facing.
Horizon had a pale green undertone which I didn't want in my room.

FB's Cornforth White is really nice but as I have red oak floors stained in Jacobean, the colour pulled a teensy tiny bit mauve. So if you have any red in your room in may do the same.

I love Balboa Mist as it's a light silvery gray with just a touch warmth to it. I also contemplated using Collingwood but it was warmer than I wanted.

Hope this helps!