The ramification-jump lifting conjecture for non-abelian cyclic p-Sylow groups

Let $p$ be a prime, let $G e \mathbb{Z}/p^n\rtimes\mathbb{Z}/m$ be non-abelian with $p\nmid m$, and let $k[[z]]/k[[t]]$ be a local $G$-extension whose $\mathbb{Z}/p^n$-subextension has upper-numbering ramification jumps $(u_1,\ldots,u_n)$, with each jump congruent to $-1\pmod m$. Ramification-jump lifting conjecture. The local extension $k[[z]]/k[[t]]$ lifts to characteristic zero. This is a conjectural sufficient condition for lifting local actions in the cyclic $p$-Sylow case; the supplied source gives no resolution status.