I agree with your thoughts on the current color. We have similar color oak cabinetry and table and we had a color specialist suggest Sherman Williams Unusual Gray. It really is a hard to describe color - not so much gray, but more like a deep sage green with a bluish hue. But it looks great with the honey oak in my opinion! Kind of a real natural feel. Here’s a photo, but the color varies a lot based on time of day, lighting, etc. which I don’t mind at all!

Get sample jars of colors you are considering and paint large pieces of foam board - observe in different lighting at different times of the day. The cool grays and warm wood tones don't do much for each other - not a clash, but they don't bring out the best. A warm gray - which is usually a green with a gray undertone or a greige can sometimes work. Also, you might look at a white with a gray undertone. The green grays help bridge the cool / warm divide that many home owners are facing as they try to update older warm toned homes with the presently fashionable grays. I am seeing much lighter grays and more whites and creams in newer design pics - a little move away from the very cool tones of the past few years.

For my own warm wood kitchen, I went with a cream with a touch of beige, but then I have not been fond of the cool grays - probably due to living in an area with too many gray days:)

This is my wood kitchens idea book - you might find some inspiration:

https://www.houzz.com/ideabooks/75202366/list/wood-kitchens

Two grays that work with warm woods - at least in these pics:

BM Maritime White:

SW Rainwashed or Sea Salt. Sea Salt, I am told, can look blue - so definitely do a sample board:

Can you remove the chair rail, and paint the walls all one color. I dont think the chair rail does anything for your kitchen. I do like the color on the top walls, not so much the blue on the chair rail.