Heller did not open pandora's box.
It is forbidden in the 2A for Federal Govt to pass laws concerning firearms.
"Shall not be infringed" restricts Federal only, The fourteenth Amendment was passed just after the Civil War To prevent states from infringing on rights guaranteed in the BOR.
That brings us to "reasonable restrictions".
A State may require of owners, of these type of weapons that they be kept secure from theft or criminal mis-use. To deny ownership by other than restricted individuals would be it violation of the several noted specific Amendments.