Polarized electron-deuteron DIS with spectator proton tagging provides a method for measuring the neutron spin structure functions with maximal theoretical control of nuclear effects. We calculate the nuclear structure factors in the longitudinal double-spin asymmetries
using methods of light-front nuclear structure. A unique feature of the spin-1 system is that spin asymmetries can be formed either relative to the cross section in all three spin states ($\lambda_d = \pm 1, 0$) or in the two maximum-spin states only ($\pm 1$, involving tensor polarization). We find that the two-state deuteron spin asymmetry at small spectator proton momenta permits accurate extraction of the neutron structure function $g_{1n}$. Such measurements could be performed at a future electron-ion collider (EIC) with polarized deuteron beams and suitable forward detectors.