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The study of the dynamics of strong interactions in the high-energy regime is a core line of frontier researches at the LHC as well as at new-generation colliding facilities. Here, the enhancement of energy logarithms due to diffractive semi-hard final states spoils the convergence of the perturbative series in the QCD running coupling, thus calling for an improvement of the pure collinear factorization that accounts for an all-order resummation of these large logarithmic contributions. Motivated by the recent discovery that inclusive emissions of heavy-flavored particles allow for clear signals of a stabilization of high-energy resummed differential distributions under higher-order corrections and scale variations, we provide novel predictions of rapidity and azimuthal-angle observables for the inclusive hadroproduction of a light meson ($η$ or $π^\pm$) in association with a heavy-flavored hadron ($Λ_c$ or $b$-flavored hadron). We calculate our observables in a hybrid high-energy and collinear factorization framework, where next-to-leading BFKL-resummed partonic cross sections are convoluted with collinear parton distributions and fragmentation functions. We consider kinematic ranges typically covered by acceptances of LHC detectors, and new ones coming from the combined tag of an ultra-forward particle at the future Forward Physics Facility (FPF) and of a central one at ATLAS via a tight timing-coincidence setup. By performing a detailed study on uncertainties associated to collinear inputs via a replica-driven analysis, as well as on ones intrinsically coming from the high-energy resummation, we highlight the challenges and the steps required to gauge the feasibility of precision studies of our processes.