We generalize and update our former top quark mass calibration framework for Monte Carlo (MC) event generators based on the e + e − hadron-level 2-jettiness τ 2 distribution in the resonance region for boosted $t\overline{t}$ $$ t\overline{t} $$ production, that was used to relate the Pythia 8.205 top mass parameter $m_t^{\mathrm{MC}}$ $$ {m}_t^{\textrm{MC}} $$ to the MSR mass $m_t^{\mathrm{MSR}}\left(R\right)$ $$ {m}_t^{\textrm{MSR}}(R) $$ and the pole mass $m_t^{\text{pole}}$ $$ {m}_t^{\textrm{pole}} $$ . The current most precise direct top mass measurements specifically determine $m_t^{\mathrm{MC}}$ $$ {m}_t^{\textrm{MC}} $$ . The updated framework includes the addition of the shape variables sum of jet masses τ s and modified jet mass τ m , and the treatment of two more gap subtraction schemes to remove the $O$ $$ \mathcal{O} $$ (ΛQCD) renormalon related to large-angle soft radiation. These generalizations entail implementing a more versatile shape-function fit procedure and accounting for a certain type of (m t /Q)2 power corrections to achieve gap-scheme and observable independent results. The theoretical description employs boosted heavy-quark effective theory (bHQET) at next-to-next-to-logarithmic order (N2LL), matched to soft-collinear effective theory (SCET) at N2LL and full QCD at next-to-leading order (NLO), and includes the dominant top width effects. Furthermore, the software framework has been modernized to use standard file and event record formats. We update the top mass calibration results by applying the new framework to Pythia 8.305, Herwig 7.2 and Sherpa 2.2.11. Even though the hadron-level resonance positions produced by the three generators differ significantly for the same top mass parameter $m_t^{\mathrm{MC}}$ $$ {m}_t^{\textrm{MC}} $$ value, the calibration shows that these differences arise from the hadronization modeling. Indeed, we find that $m_t^{\mathrm{MC}}$ $$ {m}_t^{\textrm{MC}} $$ agrees with $m_t^{\mathrm{MSR}}$ $$ {m}_t^{\textrm{MSR}} $$ (1 GeV) within 200 MeV for the three generators and differs from the pole mass by 350 to 600 MeV.