This is what happens when you get out of order. Backsplashes are the LAST decision, not a first. That said, I see no issue in your pictures. Any white is a function of the lighting in your home. .......and I would not do gray cabinetry in any scenario.

Try Chantilly Lace/Ben Moore. - its a "neutral"clean crisp white. Why does it have to be SW?

Personally, I would paint the walls the same color as the backsplash and leave the cabinets alone.

Jan, your comment about the order isn’t helpful. we had to do the counters and backsplash a long time ago and the cabinets were perfectly functional so we saw no reason to do them at the time. Now we are ready to do them and were thinking about changing colors.

It has to be SW because the cabinet company factory tints them and that’s the only line they use.

You could leave the cabinets alone and just do a color or gray on the island to tie into the backsplash? Just updating the hardware with a bright polished nickel might go a long way in making it feel more elegant + new

A statement light fixture would also finish the space!