Reply #2: I picked up a big, fine-mesh strainer from a restaurant supply store.

[eyesroll]

Pushed the soup through with a dough scraper (a spatula or wooden spoon would have worked, too).

The soup didn't end up velvety-smooth...I think a couple of the carrots might have been underdone (I've been able to get very smooth squash soup out of the strainer).

It did end up pretty thick; next time I'll probably use more stock, and make sure the carrots are very soft. Still good, though, and well tolerated by Her Pickiness.