Thyme is a woodsy herb, so is sage. They certainly won't give you the same flavor but may work. You'll never know unless you try right?

Sage and thyme would be good. Perhaps oregano would also be good. Or mint or lemon verbena. Flavors would be different, but I bet the tastes would work.

Thyme would be my choice - goes well with the other ingredients. Or just use the oregano, and when you toss in the red onion at the end, add some torn up fresh basil leaves too. (Not exactly woodsy, but would add a compatible and fresh note.)

For zucchini thyme would also be my first thought as a sub. Sage less so, that's better for meat. Oregano or marjoram yes. A mixture of flat leaf parsley and mint could be good.