A twelve-term exclusion for the small Davenport constant of $E_2\times C_3^r$

Let $E_2$ be the extraspecial group of order $3^5$ and exponent three. For every $r\ge1$, we prove that a product-one-free sequence of length $2r+11$ over $E_2\times C_3^r$ cannot contain exactly $2r-1$ central terms. Thus the critical layer with twelve noncentral terms is excluded. The proof combin