This is not a specific answer to your question but just wanted to mention that the tile that you have now plays very well with the warm and cool colors you have in your house. It looks great with the oak and great with the grey carpeting and helps tie those two together. This is also not what you asked, and I'm not usually a fan of grey cabinets, but have you considered painting your cabinets grey? I think in your house, and with those floors, if you keep them, grey cabinets would look rather smashing. As for the specific colors you mention I think they are all possibilities. Anything in the green and blue family would be very pretty. There is no substitute for trying some samplers on large paper and taping the paper to the wall to see how it looks with all your other materials. When you say you want more neutral decor...what have you got in mind? Everything looks pretty neutral now, or is paintable (like the entertainment center).

I did - our island is French Gray with a black glaze. It sometimes looks like a blue color in pictures, but it is more green than gray. (link below). At the bottom of the kitchen pictures is a link to my walk-in pantry, which is painted French Gray (last few pictures). Rococogurl is an F&B expert. If you don't get her here, you should try in Kitchens. You could also try searching AM for more F&B posts. She used them in her NYC apartment and country house. Look under House Tours > Our Houses Here is a link that might be useful: kitchen

There is usually so little wall space left in a kitchen after the cabinets and backsplash take up space that you can go with a relatively strong color without the same in your face feel that you can get in another room. With your counters, I immediately thought of Behr Antique Red or Falling Leaves. If you want to stay in the tan, I'd be sure it's something darker, with some warm undertones that work with the counters like Smoky Topaz.

Hi - don’t despair! Just give yourself a little time. Warmer bulbs won’t help here as they are likely to enhance any yellow/orange warm tones in the space. The point about Barren Plain and Calm looking a little pink is important. See on the colour wheels above, how close they sit to the Yellow-Red Hue Family? Their proximity to that neighbourhood is where the pinky/peach warmth comes from. It depends upon the quality of available light, just how pronounced those overtones will be. To help mitigate that, choose a colour from further clockwise, away from this region. So that info will help too. If you do decide to repaint, try large swatches or painted boards in your space before finalising. That way you can move them around in both sunlight & shadow to see how they will behave.