We investigate the leading-power fragmentation of triply heavy Ω baryons in high-energy hadronic collisions. Extending our previous work on the Ω_3c sector, we release the full OMG3Q1.0 family of collinear fragmentation functions by completing the description of the charm channel and delivering the novel Ω_3b functions. These hadron-structure-oriented functions are constructed from improved proxy-model calculations for heavy-quark and gluon fragmentation, matched to a flavor-aware DGLAP evolution based on the HF-NRevo scheme. For phenomenological applications, we employ the (sym)JETHAD multimodular interface to compute and analyze NLL/NLO⁺ semi-inclusive Ω_3Q plus jet distributions at the HL-LHC and FCC. This work consolidates the link between hadron structure, rare baryon production, and resummed QCD at the energy frontier.