Are you planning to paint the walls too?

Your first step could be to go to a couple of paint stores and gather lots of different greige paints chips, focussing on the ones that seem similar to the lightest colours in your counter. If you're painting the walls (which I would recommend to lighten things up), prime them. Then toss the chips on your counter at different spots (island, corner, sink, etc) and eliminate any that look not great at any spot. Hopefully you'll be left with 2-4 colours. Get sample pots of those colours and paint test boards on white foam board. Place them on the wall and against the cupboards at various times throughout the day and in various weather. You can even not notes on the back like "terrible in the rain" or " looks purple on island." You can post pictures of that here, too!

Do some research on the paint companies' websites to find suggested colour palettes to coordinate with the colours you narrow it down to.

I don't have a good color for you - had to chime in because you have the same name as my sister in law - but your are not her:)

Do have the painter show you an example of painted oak. The texture of the grain shows through but this does not bother many - just want you to know what the final look will be.

For a contrasting island, consider a blue or green - creams, tans, beiges and blues and greens work well together - rather light, airy almost costal feeling.

Should you chose not to paint, a lighter wall color will lighten your kitchen a great deal. I have an oak kitchen in my "my pics" idea book. I do not think it is your style based on your idea book, as it is more cottage / French country.

Don't waste 15K on that ER visit from a burn producing layout. Wait until you can address the kitchen as a whole, and get that cooktop off of the island. And probably get rid of the island, as it is a giant barrier between the sink and fridge. The whole kitchen is terribly inefficient.

To be honest, I would also keep the cabinets natural wood. Here is an example of a Houzz photo that I think you could use as inspiration if you decide to go that route:

Bentonville Estate Home · More Info

You could make a big difference simply by painting the walls and island to a brighter colour.

If you're interested here's the link to the search I used:

https://www.houzz.com/photos/phbr6-bp~t_709~a_14-7--16-21--17-123--19-29--20-109--65-519