  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 ($\eta$ or $\pi^\pm$) in association with a heavy-flavored hadron
($\Lambda_c$ 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.
