For starters the hinges are/were different sizes - looks like 4in on the casing, but 3in on the door.
Based on the assumption that the door casing is hinged the right way (which means that the door is hinged the wrong way) my suggestion is "something else"...
TBH I think I'd drill out the screw holes on the door to 6 or 8mm and fill them by glueing-in hardwood dowels with PVA. Once set I'd trim the dowels flush, then I'd cut some softwood slips ("Dutchmen") to fit the old hinge recesses and glue those into the hinge recesses. Whenever I do these I make them dead to length, but a couple of millimetres too wide and a millimetre or two too thick. These Dutchmen need to be applied with a strong glue, something like a D3 or D4 type PVA and you may need to hold them in place temporarily whilst the glue sets with a couple of panel pins (left sticking out). The pins can be removed once the glue has set. Finally the overhanging Dutchman is planed in using a nice sharp block plane. Once you've done repairing the door it can be shot into the opening, hinge recess markings transferred across and new hinge recesses cut (an ideal job for a router as it will let you cut recesses of consistent depth)
I know people will suggest filler (not a joiner's approach), but I can always see great gobs of filler, so to me it never looks right, and I've seen it fall out far to many times to ever be a fan of it
