Perhaps just paint the island first and see.

I think your cabinets are beautiful but if you don’t I would definitely start with the island. I’m not sure I would attempt to re-stain them. Do you know for sure if they are all solid wood?
A few colors I think would work in combination with the cherry are....Black, dark taupe, cream or BM georgian green.

I think your cabinets are beautiful as well. Personally, I would keep them as is and change out the backsplash, which is too busy IMHO. Maybe switch to a bright neutral? In any event, GL!