  We present a comprehensive study about the phenomenological implications of
the theory describing Galactic cosmic-ray scattering onto magnetosonic and
Alfv\'enic fluctuations in the $\mathrm{GeV} - \mathrm{PeV}$ domain. We compute
a set of diffusion coefficients from first principles, for different values of
the Alfv\'enic Mach number and other relevant parameters associated to both the
Galactic halo and the extended disk, taking into account the different damping
mechanisms of turbulent fluctuations acting in these environments. We confirm
that the scattering rate associated to Alfv\'enic turbulence is highly
suppressed if the anisotropy of the cascade is taken into account. On the other
hand, we highlight that magnetosonic modes play a dominant role in Galactic
confinement of cosmic rays up to $\mathrm{PeV}$ energies. We implement the
diffusion coefficients in the numerical framework of the {\tt DRAGON} code, and
simulate the equilibrium spectrum of different primary and secondary cosmic-ray
species. We show that, for reasonable choices of the parameters under
consideration, all primary and secondary fluxes at high energy (above a
rigidity of $\simeq 200 \, \mathrm{GV}$) are correctly reproduced within our
framework, in both normalization and slope.
