  We make use of hydrodynamical simulations of the intergalactic medium (IGM)
to create model quasar absorption spectra. We compare these model spectra with
the observed Keck spectra of three z>6.2 quasars with full Gunn-Peterson
troughs: SDSS J1148+5251 (z=6.42), SDSS J1030+0524 (z=6.28), and SDSS
J1623+3112 (z=6.22). We fit the probability density distributions (PDFs) of the
observed Ly alpha optical depths with those generated from the simulation, by
exploring a range of values for the size of the quasar's surrounding HII
region, R_S, the volume-weighted mean neutral hydrogen fraction in the ambient
IGM, x_H, and the quasar's ionizing photon emissivity, N_Q. In order to avoid
averaging over possibly large sightline-to-sightline fluctuations in IGM
properties, we analyze each observed quasar independently. We find the
following results for J1148+5251, J1030+0524, and J1623+3112: The best-fit
sizes R_S are 40, 41, and 29 (comoving) Mpc, respectively. These constraints
are tight, with only ~ 10% uncertainties, comparable to those caused by
redshift--determination errors. The best-fit values of N_Q are 2.1, 1.3, and
0.9 x 10^{57} s^{-1}, respectively, with a factor of ~ 2 uncertainty in each
case. Finally, the best--fit values of x_H are 0.16, 1.0, and 1.0,
respectively. The uncertainty in the case of J1148+5251 is large, and x_H is
not well constrained. However, for both J1030+0524 and J1623+3112, we find a
significant lower limit of x_H >~ 0.033. Our method is different from previous
analyses of the GP absorption spectra of these quasars, and our results
strengthen the evidence that the rapid end--stage of reionization is occurring
near z ~ 6.
