I think your ideas are very nice. If you do color on the wall, you could do a white, or white mixed counter and it would significantly brighten up the space, as well as playing nicely with a neutral gray. When you do the counter, you might consider doing a full backsplash up to the base of the cabinets. You could incorporate some "fun" color into that without having to change anything too big or expensive. Here are some similar color options to what we're talking about:

Embrace the green if you can't change it. Try a more monochromatic color scheme. Pick a light mossy green for the walls. Same tone as countertops but much lighter on the spectrum. Use darker green accents. I wouldn't pick a gray toned color for your walls since your green is a warm tone your cabinets are warm and your wood work is warm toned, and gray is a cool tone.

Be careful of cool grays with warm wood tones - neither brings out the best in the other. That is why white painted cabinets /trim and dark wood tones are usually used with gray. Creams, creamy beige and blues and greens look good with oak. The blues and greens can have gray undertones and that works.

One of your pictures shows a yellowish wall color and yellows aren't always the best for oak. The other shows a cream color on my monitor which looks nice. I am assuming that my monitor is reading the same color different ways in different lighting.

Here is an article about "grays" that go with oak - most are really blues or greens. I like some but others are in my opinion not the best look - but I guess will work to be "on trend".

http://www.housekaboodle.com/gray-paint-colors-with-wood-trim/

Also, change bulbs to LED warm or sunlight if you have not already as the curly Q fluorescents tend to make the oak look more yellow.

Over time consider changing appliances to white (or stainless) as they die. I have white with my oak and it really lightens the space. Also, for a change up, consider a hood vent - you might just be able to install a vent insert under the cabinets. I think you have a really nice kitchen:)

Thanks so much for the ideas. The backsplash is something I've been meaning to do - after I paint!