Thermal relic dark matter below ∼10 GeV is excluded by cosmic microwave background data if its annihilation to visible particles is unsuppressed near the epoch of recombination. Usual model-building measures to avoid this bound involve kinematically suppressing the annihilation rate in the low-velocity limit, thereby yielding dim prospects for indirect detection signatures at late times. In this work, we investigate a class of cosmologically-viable sub-GeV thermal relics with late-time annihilation rates that are detectable with existing and proposed telescopes across a wide range of parameter space. We study a representative model of inelastic dark matter featuring a stable state χ1 and a slightly heavier excited state χ2 whose abundance is thermally depleted before recombination. Since the kinetic energy of dark matter in the Milky Way is much larger than it is during recombination, χ1χ1→χ2χ2 upscattering can efficiently regenerate a cosmologically long-lived Galactic population of χ2, whose subsequent coannihilations with χ1 give rise to observable gamma-rays in the ∼1 MeV−100 MeV energy range. We find that proposed MeV gamma-ray telescopes, such as e-ASTROGAM, AMEGO, and MAST, would be sensitive to much of the thermal relic parameter space in this class of models and thereby enable both discovery and model discrimination in the event of a signal at accelerator or direct detection experiments.