I'd add more straw, enough to cover the newspaper throughout, to give them more traction.
Agree about securing the heat lamp with more than the clamp. If you have a shower rod above, hang a chain from the rod down to the hanging loop of the lamp, that way IF the clamp fails at least it won't fall in and start a fire.
Also you'll need a cover on the tub very soon to keep chicks from popping out. Back when I brooded in a bathtub, I covered it with a rectangle of wire mesh (like hardware cloth) and then taped cardboard around the edges so it wouldn't scratch the tub.