The spin structure function of the neutron is traditionally determined by measuring the spin asymmetry of inclusive electron deep inelastic scattering (DIS) off polarized 3He nuclei. In such experiments, nuclear corrections are significant and must be treated carefully in the interpretation of experimental data. Here we study the feasibility of suppressing model dependencies by tagging both spectator protons in the process of DIS off neutrons in 3He at the forthcoming Electron-Ion Collider (EIC). This allows for a reconstruction of the momentum of the struck neutron to ensure it was nearly at rest in the initial state, thereby reducing sensitivity to nuclear corrections and suppressing contributions from electron DIS off protons in 3He. Using realistic accelerator and detector configurations, we demonstrate that the EIC can probe the neutron spin structure from xB of 0.003 to 0.651. We find that the double spectator tagging method results in reduced uncertainties by a factor of 4 on the extracted neutron spin asymmetries over all kinematics and by a factor of 10 in the low-xB region, thereby providing valuable insight into the spin and flavor structure of nucleons.