  Cubic silicon-carbide crystals, known for their high thermal conductivity and
in-plane stress, hold significant promise for the development of high-quality
($Q$) mechanical oscillators. Enabling coherent electrical manipulation of
long-lived mechanical resonators would be instrumental in advancing the
development of phononic memories, repeaters, and transducers for microwave
quantum states. In this study, we demonstrate the compatibility of high-stress
and crystalline (3C-phase) silicon-carbide membranes with superconducting
microwave circuits. We establish a coherent electromechanical interface for
long-lived phonons, allowing precise control over the electromechanical
cooperativity. This interface enables tunable slow-light time with group delays
extending up to an impressive duration of \emph{an hour}. We then investigate a
phononic memory based on the high-$Q$ ($10^{8}$) silicon-carbide membrane,
capable of storing and retrieving microwave coherent states \emph{on-demand}.
The thermal and coherent components can be distinguished through state
tomography in quadrature phase space, which shows an exponential increase and
decay trend respectively as the storage time increases. The electromechanical
interface and phononic memory made from crystalline silicon-carbide membrane
possess enticing attributes, including low microwave-induced mechanical
heating, phase coherence, an energy decay time of $T_{1}=19.9$~s, and it
acquires less than one quantum noise within $\tau_{\textrm{coh}}=41.3$~ms
storage period. These findings underscore the unique opportunities provided by
cubic silicon-carbide membrane crystals for the storage and transfer of quantum
information across distinct components of hybrid quantum systems.
