The ceiling is beautiful. The gray in the rest of the space clashes with it, but the ceiling does warm it up. If the ceiling were white too that wouldn't be as interesting. It would look like a flipper got to it.

I don’t think whitewashing will be very complementary. White ceiling, natural beams work below, because of the type of ceiling and beams.

The few pictures I could find with your type of ceiling had painted beams with the whitewash. Your ceiling is much nicer.

If it were me, I’d leave ceiling as is and focus on how to make the space feel less broken up; paint the dark grey above sliding doors and lower island, and walls/trim a warm white. The white molding above the dark wall tile as well as the white strip in ceiling are sticking out big time. The less interruption the better.

If you really hate the wood’s stain, suggest painting the entire ceiling. Space above sliding doors should be wall color.

IMO the wood was added to a ceiling that is too low to have done that so I would paint the whole thing white not a wash but white it is IMO oppressive in that space BTW get some good lighting it that kitchen for sure and a counter depth fridge