A vortex-glass transition due to point disorder in Layered superconductors is studied for the case with an applied field parallel to the layers. Our calculation of tilt responses indicates that, irrespective of the magnitude of the field, the resulting glass phase, Josephson-vortex-glass (JG), should have a transverse Meissner effect, as in a planar splayed glass phase, only for a tilt perpendicular to the layers. Further, focusing on the high field (and/or high anisotropy) region B root Gamma > phi(0)/d(2), where Gamma is the mass anisotropy in the Lawrence-Doniach model, the JG transition line T-JG(B) is shown to have a similar form to a B-T line following from the disorder-free Lindemann criterion and to decrease with increasing B root Gamma,in marked contrast to the disorder-free melting line insensitive to B root Gamma in such the high field region. This TJG(B) line seems to have been recently observed in a.c. susceptibility and in-plane resistivity measurements in BSCCO and qualitatively explains a field dependence at lower temperatures of previous BSCCO resistivity data showing the so-called in-plane Lorentz force-free behavior.