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Interaction between quasiparticles of a different nature, such as magnons and phonons in a magnetic medium, leads to the mixing of their properties and the formation of hybrid states in the areas of intersection of individual spectral branches. We recently reported the discovery of a new phenomenon mediated by the magnon-phonon interaction: the spontaneous bottleneck accumulation of magnetoelastic bosons under electromagnetic pumping of pure magnons into a ferrimagnetic yttrium iron garnet film. Here, by studying the transport properties of the accumulated magnetoelastic bosons, we reveal that such accumulation occurs in two frequency-distant groups of quasiparticles: quasiphonons and quasimagnons. They propagate with different velocities in different directions relative to the magnetization field. The theoretical model we propose qualitatively describes the double accumulation effect, and the analysis of the two-dimensional spectrum of quasiparticles in the hybridization region allows us to determine the wave vectors and frequencies of each of the groups.