I was under the impression that an "amnesty period" was still allowed under the law. Did the Hughes Amendment eliminate that?
Yes, it effectively did, though in practicality the amnesty ended years before.
Up until about 68, if you "discovered" (or were caught) an unregistered, untaxed machine gun, you could pay the tax, register the gun, and keep it.
It was generally considered a minor tax boo-boo and seldom were criminal charges brought. This changed around 68 (if I remember correctly, but I might have the year wrong..) anyway, the Govt decided to treat an untaxed machine gun as a criminal matter (10years prison, $10,000 fine, felony conviction) At that time, there was a 6 months "amnesty" so that if you hadn't previously registered and paid the tax on your machine gun, you could do so during the amnesty period without facing criminal charges.
More than a few people did just that.
However, the Hughes Amendment ended any additional registry for civilian owners. If the gun was not registered with the government by May 19, 1986, it would not be allowed to be registered in the civilian registry. New guns could be made, and registered, for sale only to the military and police. Machine gun dealers could have them, or make them, as "dealer samples" to demonstrate the weapons to authorized buyers, but these guns cannot be sold to private individuals.
the ATF does not have the authority to modify the federal definition of "machine gun," and bump stocks do not meet the NFA/GCA definition.
I, personally agree with this, however, the administration apparently does not, they believe they have the authority to administratively change the definition, and they are DOING it. Until/unless a court rules against them, they will get away with it.