how do the rest of you wash stuffed animals?

Check the label first. Anything with a music box, battery pack or glued-on eyes isn't going in a washer - surface clean those with a damp cloth and a little soap. For the rest, put them in a pillowcase tied shut or a laundry bag, gentle cycle, cool water. Air dry rather than tumble, heat can melt the stuffing or the plastic bits. Give them a squeeze and a fluff while drying so the filling doesn't clump.