My Glovebox lid is fastened to a Piano hinge from the inside, but the hinge is secured to the dash with the fasteners that can seen from under neath.
By removing the hinge fasteners can you tilt the lid from the bottom and undo the 2 strike screws.
Please note: I am referencing this material from my 64 Galaxie.
Glove box liners are secured from the inside----which means the screws ends are on the outside of liner, and can be turned with pliers.