I am terrible at choosing paint colors so I am not much help. She thinks she wants a true brighter white. Think modern Scandinavian.

The problem is in a north facing room it will never read truly white. What color is the carpet?

The carpet is a light beige.

If you want HRW, you're pretty much limited to SW's Duration, you'd want the matte finish because anything glossier will be shiny - too shiny for walls IMO. If they try (emphasis on try) to make HRW in other products, they have to shoot a lot of white into the can which means the hide will be affected and you'll have to do three coats.

If you're going to be in that price bracket, you might as well get a couple gallons of full spectrum white which will maximize the quality of north light you have to work with.

Ellen Kennon's colors are mixed in PPG's Manor Hall, you can call or buy a set of samples online. Or C2 Paint is another full spectrum brand. C2's Sheer C2-804 would compliment a Scandinavian design aesthetic.