We present suppression predictions from our pQCD-based energy loss model, which receives small system size corrections, for high-\(p_T\) \(\pi\), \(D\) and \(B\) meson \(R_{AB}\) as a function of centrality, flavor, \(\sqrt{s_{NN}}\), and \(p_T\) from large to small collision systems at RHIC and LHC. A statistical analysis is used to constrain the effective strong coupling in our model to available high-\(p_T\) suppression data from central heavy-ion collisions at RHIC and LHC, yielding good agreement with all available data. We estimate two important theoretical uncertainties in our model, stemming from: the transition between vacuum and hard thermal loop propagators in the collisional energy loss, and from the angular cutoff on the radiated gluon momentum. We find, consistently, that the extracted \(\alpha_s\) remains relatively unchanged across heavy- and light-flavor final states and across central, semi-central, and peripheral collisions. We make predictions from our large-system-constrained model for small systems and find good agreement with photon-normalized \(R^{\pi^0}_{d \text{Au}} \simeq 0.75\) in \(0-5\%\) centrality \(d\) + Au collisions by PHENIX. However, we find strong disagreement with the measured \(R^{h^{\pm}}_{p \text{Pb}} \gtrsim 1\) in \(0-5\%\) centrality \(p\) + Pb collisions by ALICE and ATLAS; we argue that this disagreement is due, in large part, to centrality bias. We make predictions for the ratio of suppression in \({}^3\)He + Au and \(p\) + Au collisions, which may in the future be used to disentangle final- from initial-state suppression in small systems. We then compare our results to various subsets of data, which allows us to estimate the preferred: low-\(p_T\) scale at which non-perturbative processes become important, scales at which the strong coupling runs, and scale at which vacuum propagators transition to thermally modified propagators in collisional energy loss.