Strong western afternoon sun will give any white a more yellow tone, and Simply White is a warm, creamy (ie very slightly yellow) toned white although not strongly so to start with - I have it in a north facing room with dark brown floors, and a warm cream/ blue rug, and pale yellow curtains -- it is quite white in there, doesn't appear yellow at all unless I put something that is white white (like printer paper) up against it.
My living room is painted in Navajo White which is distinctly a pale yellow-tan; but in the afternoon when light reflects off the neighbor's red house, the walls look rather pinkish! No color that I could have chosen would defeat that effect.
I think that the advice about using 3000-4000K light bulbs is spot on. Lower color temp bulbs make everything look more yellow.
I am not sure that adding a gray gray to the mix will make the warmth of Simply White less noticeable, it might in fact emphasize it. Classic Gray in some photos looks too gray, but in others seems a nice warm beigey shade that might work very well.
Surrounding the Simply White with somewhat stronger, warm (not cool!) colors will emphasize its white quality. Bringing in furnishings always helps to tone down a wall color. Be careful with your furniture selections to be sure you aren't bringing in clashing tone - the right swatch looks too cool (blue gray) to me.
Q