I think painting the uppers and staining the lowers will not give you as cohesive a look as doing one or the other. The best solution in terms of color partly depends on whether you're planning to keep the flooring and the dark wood island as is.

I like a two-toned kitchen, but it may feel a bit modern for your traditional house unless you can find a bit of gravitas for the whole. Let me look for some photos...

I was wondering about painting them all something like the color of your sideboard? I have a two tone kitchen (off white with quarter sawn oak lowers) but I think your kitchen whould be lovely as a serene backdrop to your dining room.

I can work with the traditionality, but most of the two-tone examples have more of a (French?) farmhouse feel, which still may or may not feel at home with your formal furniture pieces.

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It's possible, though, that the style of the cabinets and the look of the current island will be enough to bridge the gap even if you kitchen gets a bit of a transitional edge going...

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Just one other idea to throw out there: you could paint your uppers white and use the base cabinets to bring in some of the blue(s) from your dining room:

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