Your cabinet are beautiful. I would leave them until last. Get new appliances as they will lighten up the room. Then the floor and counter and backspash. Paint if you must, but your cabinets seems really nice. What if you just painted the uppers or the lowers for contrast and design style?

Do green rug, towel. It will pop. Or even teal.

I like your ctops. I like quartz & a white/ gray marble look.

Yes, your instincts are correct. The reason why things are not working is because the cabinet color really is a warm tone and the gray counters are gray; a cool tone.

You can make your kitchen work by simply replacing the counters with a granite which has black (to tie in the existing black appliances), off white (to tie in the cabinet counters) and tans (to tie in the floor).

The cabinets look nice - in the picture, but I realize that may not be the case in reality. Are these wood cabinets that were painted, or original factory painted cabinets? I was wondering if this was a case of someone trying to update the kitchen to sell - went with cream and gray, and just missed. I agree to get the countertops first and then see if you still think you need to paint the cabinets, unless they just need to be painted because they need it. You can always start with white primer to see if the white is too stark.

The flooring should be in harmony with the countertop. A warm countertop would fix everything, in my opinion . Countertop should be no darker than the floor. I see no need to paint the cabinets. It looks like the walls are gray. I would change that but not until after countertop is replaced. Since you are so concerned with your color choice why not let us know what you are considering?

Putting together a kitchen color palette can be challenging!
Here is a great article that might help: Kitchen
Color Palette

I don't think it will be too much white. These are Dove White by BM. Something like this shouldn't be a problem with your floor tile.

To my eye, the flooring is wrong for the cabinets (which seem pretty) with the counter. That's not to say that you shouldn't change everything, but maybe start with one thing (not to match anything else) and go from there. In my mind, I would start with the countertop, as that is a big expense. If you choose to take out the floor, do something lighter like a travertine.

You have cool vs warm mix going there, that is why they are visually not blending. If the quality of your cabinets is good - they look nice in the photo - I would suggest changing the counter top to a quartz that has grays and tans, and taking off that backsplash. Looks like your walls above are grey too - but they are a cool grey. Something along the lines of Revere Pewter would warm up those walls and is less expense/mess than ripping out a tile floor. http://pentalquartz.com/products/cashmere/ to look at quartz options.

Another option would be to paint the cupboards a Dove White, if you don't like the current warm ivory tone.