Setting aside that this is a brute force attack on the hash rather than the key, only made possible because of dropped bits, the method here doesn't apply. It depends on there being no initial salt. All further iterations of sha1 can be salt free and still safe from this attack since you are not able to feed an arbitrary string into the key function.

Edit: Thinking about it I should be more specific, especially since I got confused myself for a moment. The key is that you don't salt the same way at each step. So a unique salt per iteration is great, salting the first iteration is fine, salting zero or all iterations with a particular salt ruins you.