Sorry but the Iowa and her sisters had plenty of ammo
http://www.navweaps.com/Weapons/WNUS_16-50_mk7.htm
11) A 1981 inventory of naval ammunition storage facilities found that there were 15,500 HC projectiles, 3,200 AP projectiles and 2,300 practice rounds in stock.
And given that they stayed in service there were new projectiles in development for those guns that may have increased that total
Even divided by four thats 3800+HC and 800 AP projectiles per ship - and with the radars installed on them during the 1980's they basically would be on target from the first salvo
or to say it another way - each ship had enough ammo allocated to basically sink most of the Soviet surface fleet all by itself