How do I make this quick-bread recipe less moist?
Not sure what done is for this; maybe you just need to bake it longer? That should drive out water—though possibly it will cause other problems. But probably it'll be OK since you can grill it.

I think getting some water out of the shredded carrots is the first thing to try—they have a lot of water (like all vegetables). Patting them dry will remove some. Pressing them between dry towels/paper towels will remove more. Roasting (or sautéing) them can remove even more (and will change the flavor). Or you could use a food dehydrator or low oven to just dry them.

Reducing the amount of carrot may help too, but that will again alter the flavor.

Another thing that might help: I suspect you have the eggs for binding &amp; richness. That's mostly the yolk—you could try leaving out some or all of the whites (using the yolk only).