Couldn't hurt to look at a neutral greigy white like BM Classic Gray. Might provide more balance with the floor and backsplash.

What about changing the backsplash? Any ideas?

Paint upper cabinets light grey.
Paint/stain lower cabinets dark ebony

Your ideabook is full of light grays and airy designs. I suggest a very pale silver gray instead of a greige paint would be a much trendier update that would coordinate well with the backsplash, flooring and cherry cabinets.

I wouldn't paint those cabinets, they are lovely. I feel like the gray tones of the backsplash and counter are competing with the warm beige of the floor. Personally I'd like to get rid of the grays and replace the backsplash and counter with something that has more of the beige tones, or maybe a dark counter and a beige backsplash. I also don't like the square detail in the floor but you'd have to replace the whole floor to get rid of that. Add some color and personality with window treatment, colorful items on counter. Maybe add some lighting other than the cans for additional personality. If you want to change look of cabinets consider switching out hardware, although personally I like what you have. But I would never paint the beautiful wood tones especially for another generic greige kitchen.

Continue to work with the beautiful cherry cabinetry. It appears the space is mostly warm tones in nature. . .as greige goes, check out Sherwin Williams Mega Greige SW 7031. Try adding a window treatment, artwork, and accent pieces for pops of color. Simple accessorizing can make a huge impact overall.