You are on to something. What if FR commissioned the crafting of an appropriate medal, and the process of nominating and adjudicating candidates of Counter Jihadist Heroes?
I'm not sure what America should do - Australia's honours system evolved out of the fact we are a Monarchy, and for us, it's appropriate. A Republic might make different decisions for perfectly valid reasons. But I do note that you do have some elements of a civil honors system already - the Presidential Medal of Freedom and the Presidential Citizens Medal.
I think our system is appropriate because it provides very clear, very real formal recognition of both heroism and other forms of service by civilians. I think America could probably find such a tradition worth having.