Before revision:  For n of this form, this nearly matches  the best known bound of \exp\big(O(n^{1/3})\big) for standard trace reconstruction \big(O)}\big) .
After revision:  For n of this form, this nearly matches the best known bound of \exp\big(O(n^{1/3})\big) for standard trace reconstruction when this paper was initially released. We note, however, that Chase very recently improved the standard trace reconstruction bound to \exp\big(O)}\big) .