Now this I know about the modern hollow core doors are a bugger to separate as you have found out...If you can get your hands on the older hollow core doors they have no cardboard only real wood ( no pics sorry) there is the frame around the whole door and a wide block across the centre where the handle and or lock is. The glue that is holding the ply on is only the old animal glue and separates easy with chisel or old wide blade knife... and the doors down here in NZ is/was 4mm Rimu ply...
Oh I cut the out side edge first then the centre piece then attack the two halves by pulling them apart and/or using the chisel/knife...