Well, really you need to consider much more than the kitchen color for your great room/dining room. Such as the wood tones of your furniture, fabrics used, volume of room, natural light, atmosphere you wish to achieve, architectural features, etc. And the fact that these rooms are separate gives you more flexibility.
That said, here's how I would approach it. I would use an analogous hue in the same value and tone. This gives you the greatest continuity. Analogous colors are adjacent on the color wheel. Value is light to dark. And tone in this case is purity versus gray influence.
I would do a blue that has some yellow in it which will relate it back to Kittery Point.
I suggest BM HC-143 Wythe Blue. It has a similar value and tone. It's an analogous hue but distinctive.
Again, this suggestion satisfies your desire for a smooth transition color, but may not be best based on the other needs of the room as I stated above.
Good luck!