Ehrich, First, before removing any hardware,                                                          mark around any hinge /bracket or fixture            with a sharp knife or pencil 

That alone will insure that you will drill new holes exactly where the factory located them

Even marking the outlines of the hinge holes will help.                                         
Naturally,if these marks will show on the outside,  you can place temporary strips of masking tape around the fixture instead of leaving marks 
to 'Outline' the fixture.

Gluing and plugging the old holes are             the best way to go.

  Longer screws will work, so long as they          don't come through the finished side.

I would not try using wider or thicker screws 
BUT, I reccomend replacing the original screws  withFlat head sheet metal screws.
 (Of the same thickness.) 

IE:  #6  # 8  #10 x 3/4" or !'  etc.                                                                     These screws are not tapered and                 won't work loose like the old tapered wood screws.

I buy( From a shoe repair shop) a package         of square wooden shoe nails just for this purpose. 

They can be dipped in glue and driven into the old holesand more can be added as needed.

 After all the glue has dried,                      sand down any protruding plugs                     THEN, place the hinge inside the markings          and mark the centers of all the screw holes.                                     

 (Since drilling new smaller starter holes          in he plugged holes invites wandering              of the drillbit, I use a fine awl to first         prick the center to keep the drill bit from 'Straying'