In this paper we improve the semiclassical treatment of bosonized QED around a large-Z nucleus. In particular, the ground state of the system is approximated by means of a variational method based on a wider class of coherent trial states. These are defined in terms of excitations for a vacuum appropriate to a free boson theory with a space-dependent mass \ensuremath{\kappa}/r, where r is the distance from the nucleus and \ensuremath{\kappa} is a dimensionless constant. Our key issue consists in treating \ensuremath{\kappa} as a further variational parameter. The expectation value of the Hamiltonian is computed via a normal-ordering technique analogous to that used by Coleman in a similar context. The reliability of the improved treatment is suggested by our satisfactory prediction for ${\mathit{Z}}_{\mathrm{cr}}$, the critical value of the nuclear charge corresponding to the instability of the conventional neutral vacuum.