Quotient structure conjecture for del Pezzo bundles with high-multiplicity fibers

Let $f\colon X\to Z\ni o$ be the germ of a del Pezzo bundle, and let $m_oF_o=f^*(o)$ be a fiber of multiplicity $m_o$, where $m_o\geq 5$ and $F_o$ is of type $I_{2,3,6}$ or $I_{5,5}$. Quotient structure conjecture. The morphism $f$ is a quotient of a Gorenstein del Pezzo bundle by a cyclic group acting freely in codimension $2$ on $X$. This describes the structure expected for del Pezzo bundles whose fibers have multiplicity at least $5$; the supplied text does not state whether the assertion has been proved or remains open.