5.56 pressures are higher than .223.
.308 pressures are higher than 7.62.
So if you are concerned, you can still safely shoot .223 in a 5.56 and 7.62 in a .308.
I shoot 5.56 in my .223 guns all the time. And .223 in my 5.56 guns.
I shoot 7.62 in my .308 guns, but not the other way around. Not because I don't think it's safe, but because I'm cheap.
If at first you don't succeed, shoot, shoot again.