.223??? Nope. Have seen 7,62 and .303 ball bounce off a croc's head - and we were not culling big ones either! A good blunt nosed 30 cal will do the job (barnes banded solid) or preferably a good .300 mag.
Personally I just use my 9,3 x62- but then I favour a spine shot not a head shot. too many 'funny's with head shots depending on angle. For a client at say 80m from a rest, you can usually get a good angle at a flat(ish) spot on the side of the head. Culling them at night from a boat...you take whatever shots you can, and dang are those scutres a) hard and b) well sloped to deflect pointed bullets!
The Egyptians used the back skins as armour before the invention of chain mail.....