Gray Owl is a green gray, so if you use something with a purple or orange undertone, that will intensify the green cast. If you use something with a blue or green base, it will harmonize, and visually erase the green cast. BM suggests Silver Spring. Or maybe something like a SW Quietude or Rainwashed. See how the purple and yellow based colors bring out the green in Gray Owl?

I'd look for a tinted white/ barely there gray, as I prefer a white/neutral kitchen. as in this entry space gray door and light walls. You need to know the tones of gray cabinet paint- cool or warm.. Take a cabinet door to BM or Sherwin Williams or other paint store.....Ask staff to match it to one of their colors. Research palettes with that color. SW has several books that have pre-coordinated palettes --nearly all have a few gray shades.... Or web search example below. My current project: Laundry/ utility room was decided on colors we liked SWSea Salt and Eider White. The cabinet color is SWMindful Gray after reviewing many paint swatches. Then, last night I came across this, which reinforced the selections ETA. I hated the BM and SW color visualizers, those programs were not helpful. Search kitchens with gray cabinets. If a page doesn't have wall paint details, then save the image and use a Reverse Image search, which will show you to other sites with that image, like Instagram. It takes a bit of effort, but it is well worth it . Try: https://www.reverseimagesearch.com 

Not your desired response but the swap of counter and backsplash to light choices along w already light floors would accomplish nearly all your goal of a less dark kitchen. I’d absolutely do that wait on the expensive cabinet paint aspect. Walls can wait It’s just paint.

A lot of people have used Gray Owl paint on the walls, and you can find photos in the archives here at Houzz or with a basic Google search. Sea Salt is a pretty specific green, so I'm not sure it would go very well with Gray Owl which is a complex color that can lean in several different directions including toward blue depending on the pairing. Your best option would be to buy sample cans of both and paint on boards that you can locate in different areas of your space in all the lighting conditions you'll encounter throughout the day to see how well they combine in your space.