  We introduce a particle-number reprojection method in the shell model Monte
Carlo that enables the calculation of observables for a series of nuclei using
a Monte Carlo sampling for a single nucleus. The method is used to calculate
nuclear level densities in the complete $(pf+g_{9/2})$-shell using a good-sign
Hamiltonian. Level densities of odd-A and odd-odd nuclei are reliably extracted
despite an additional sign problem. Both the mass and the $T_z$ dependence of
the experimental level densities are well described without any adjustable
parameters. The single-particle level density parameter is found to vary
smoothly with mass. The odd-even staggering observed in the calculated
backshift parameter follows the experimental data more closely than do
empirical formulae.
