https://en.wikipedia.org/wiki/National_Firearms_Act
I don't know of any provision in the National Firearms Act that allows an exemption of registering NFA firearms for militia use.
Also of note is the fact that the Supreme Court has argued in favor of upholding the constitutionality of the National Firearms Act, because Short Barreled Rifles were said to have 'no militia use' so it was fine to charge an insane amount of money for transferring ownership of one of these guns to another person. Yet Machine Guns and Short Barreled Rifles are also regulated heavily by the act, but it's fine to infringe on them...
$200 in 1934 is worth about $3000 for the gun changing ownership. Anytime you sell the gun, you had to pay a tax of $3000. That sounds like an infringement to me if these have a militia use. It was upheld when challenged in court, even though back then and even today NFA firearms are widely used in the military.
This is an incredibly complex piece of legislation that even the regulatory agency, the ATF, flip flops on its definitions. On a whim they have decided a device that 'can' be mounted on your shoulder turns your pistol into a short-barreled rifle, a huge fine and potential 10 years in jail for 'manufacturing' (i.e. buying and screwing onto your gun) several months after sending out letters reassuring everyone that the device was NOT necessary to register under the act.
I don't trust flip-flopping agencies who cannot make up their mind on laws, creating huge consequences for anyone that believes their first judgement not to infringe on the right to keep and bear arms. There are no judges, there is no new legislation clarifying anything since the law was written over 80 years ago. All we have are these bureaucrats who decide what is and isn't legal based on how bitchy they feel one day. Their reasoning for tons of their classifications is circular.