How to make cookies less cake-y

For future questions of this nature, reference Shirley Corriher's Bakewise (if you don't have it, get it and put it next to On Food and Cooking). I use it all the time for things like this.

Try decreasing the sugar by 1/4 cup and adding 1/2 cup of light corn syrup. The liquid sweetener helps the cookie maintain its chew by adding moisture.

This is sort of an add-on question, but don't you think these particular cookies are going to be pretty cakey no matter what because the zucchini provides so much moisture?

Here are some tips on cookie texture alteration from Cook's Illustrated. Hope it helps.
By adjusting key ingredients, you can change the texture of any cookie recipe.

If you want chewy cookies, add melted butter. Butter is 20 percent water. Melting helps water in butter mix with flour to form gluten.

If you want thin, candy-like cookies, add more sugar. Sugar becomes fluid in the oven and helps cookies spread.

If you want cakey cookies, add more eggs. Yolks make cookies rich, and whites cause cookies to puff and dry out.

If you want an open, coarse crumb and craggy top, add baking soda. Baking soda reacts quickly with acidic ingredients (such as brown sugar) to create lots of gas bubbles.

If you want a fine, tight crumb and smooth top, add baking powder. Baking powder works slowly and allows for an even rise.

Also, reducing the baking time by a minute or 2 often produces a chewier cookie. ;o)

Up the fat, lower the dry ingredients. Play with that relationship. I feel a cookie sandwich coming on ...