Yes, but only one of them. For the typc of scrutiny the DoJ says is appropriate for the second amendment, heightened security, it's the *only* one required.
I might have to read it again to comment confidently.
But I thought that the "reasonable regulation" claim was equivalent to "rational basis"; that is, the government need only show that there is a reason for the law. It isn't even necessary to show that the law would be effective.
"Compelling state interest" would at least create a burden on the state to demonstrate that the laws are effective. I'm certainly not aware of any felon who decided not to commit another crime because he couldn't get a gun. How would one prove that a waiting period was beneficial without considering both the cooling off effect, if any, and the effect of denying a person a needed weapon for days.
Even the machinegun ban fails, since the number of crimes committed prior to the ban on manufacture was miniscule.