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We present a comprehensive study about the phenomenological implications of the theory describing Galactic cosmic-ray scattering onto magnetosonic and Alfvénic fluctuations in the $\mathrm{GeV} - \mathrm{PeV}$ domain. We compute a set of diffusion coefficients from first principles, for different values of the Alfvénic 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 Alfvénic 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.