I'm not recommending anything with this comment, but only pointing out some empirical findings. PAM has been tested at ten times recommended dosage, and found to be safe.
One way that permethrin can be dangerous is if it is not allowed to dry on the treated surface before reintroducing the animal (so, it is absolutely important to let it dry thoroughly, as the label states). Permethrin in solution is moderately dangerous; when it has dried on a surface it is quite immobile (this is why we can soak clothing in it safely):