The Compton double-polarization observable \(\Sigma_{2z}\) has been measured for the first time in the \(\Delta(1232)\) resonance region using a circularly polarized photon beam incident on a longitudinally polarized target at the Mainz Microtron. This paper reports these results, together with the model-dependent extraction of four proton spin polarizabilities from fits to additional asymmetry data using dispersion relation and chiral perturbation theory calculations, with the former resulting in: \(\gamma_{E1E1} = -3.18 \pm 0.52\), \(\gamma_{M1M1} = 2.98 \pm 0.43\), \(\gamma_{E1M2} = -0.44 \pm 0.67\) and \(\gamma_{M1E2} = 1.58 \pm 0.43\), in units of \(10^{-4}~\mathrm{fm}^{4}\).