Single-particle finite-size errors remain a central obstacle in quantum Monte Carlo (QMC) simulations of periodic systems, conventionally reduced via twist averaging (TA). Here we introduce Good-$\Gamma$ (GG) particle numbers as system sizes $N$ at which the $\Gamma$-point Hartree–Fock (HF) energy of the high-density two-dimensional uniform electron gas (2D UEG) lies anomalously close to its thermodynamic-limit (TL) value. All results in this work concern the 2D UEG in its high-density Fermi-liquid regime, $r_s=1$–$4$. We systematically investigate the kinetic- and exchange-energy errors, $\Delta KE(N)$ and $\Delta EX(N)$, that underlie this one-body finite-size-error cancellation across four densities and both spin polarizations. We then compare diffusion Monte Carlo (DMC) energies extrapolated to the TL from GG-$N$ sequences against twist-averaged extrapolations at the same densities and polarizations, finding agreement to within a fraction of a millihartree in every case, independent of whether a $1/N$ or an $N^{-5/4}$ extrapolation form is used.