  We calculate the leading-twist helicity-dependent generalized parton
distributions (GPDs) of the proton at finite skewness in the
Nambu--Jona-Lasinio (NJL) model of quantum chromodynamics (QCD). From these
(and previously calculated helicity-independent GPDs) we obtain the spin
decomposition of the proton, including predictions for quark intrinsic spin and
orbital angular momentum. The inclusion of multiple species of diquarks is
found to have a significant effect on the flavor decomposition, and resolving
the internal structure of these dynamical diquark correlations proves essential
for the mechanical stability of the proton. At a scale of $Q^2=4\,$GeV$^2$ we
find that the up and down quarks carry an intrinsic spin and orbital angular
momentum of $S_u=0.534$, $S_d=-0.214$, $L_u=-0.189$, and $L_d=0.210$, whereas
the gluons have a total angular momentum of $J_g=0.151$. The down quark is
therefore found to carry almost no total angular momentum due to cancellations
between spin and orbital contributions. Comparisons are made between these spin
decomposition results and lattice QCD calculations.
