Well here’s the issue, OP says the range doesn’t allow “steel core” ammo. So if that is the actual letter of the law, bimetal/copper washed steel jacket ammo should be fine, magnetic or not.
But since they use a magnet to test, being magnetic matters.
I have a case of Yugoslavian 7,62X54R that is brass case and copper jacket bullet. I just tested it and none is magnetic. Damn nice ammo.