The first thing to have done is to have granted Snowden immunity so that what he was holding back would not be distributed to America’s adversaries.
The second thing to have done is to have convened a federal commission to investigate how this monitoring of American citizens got so out of hand (don’t care about non-Americans as they are not covered by the Constitution’s Bill of Rights) and to come up with proposals for collecting intelligence data while preserving maxim liberties and rights to American citizens.
The third thing (to run concurrently with the second thing) to have done is to have rounded up all those who were caught up in subverting the US Constitution and put them on trial while allowing certain unclassified portions of the trial to be broadcast internationally. The broadcast would showcase how America deals with those who violate its citizens rights. Such a display would set an example for the rest of the world to follow.
Of course Snowden would have been compelled to turn over all that he had that had not yet been published or somehow disclosed. So the damage to national security could have been minimized. Instead the US government scared Snowden into running away.
This isn't really the case — you see, the Constitution doesn't apply to citizens, it applies to the government.
You can see this clearly in the preamble to the Bill of Rights:
THE Conventions of a number of the States, having at the time of their adopting the Constitution, expressed a desire, in order to prevent misconstruction or abuse of its powers, that further declaratory and restrictive clauses should be added: And as extending the ground of public confidence in the Government, will best ensure the beneficent ends of its institution.The first amendment, for example, further restricts the government, particularly congress, from enacting certain laws.
shall not be infringed— interestingly, this also restricts the taxation powers of the unamended Constitution, so even the BATFE's NFA Class III licensing/taxation scheme is illegitimate.
Since the Bill of Rights, properly understood, restricts the government's actions it is foolish to claim that non-citizens are exempt. For example, the sixth amendment provides that In all criminal prosecutions, the accused shall enjoy the right to […] be informed of the nature and cause of the accusation
— under your model the sixth does not apply to criminal prosecutions, but to citizens who are prosecuted.
Besides this, there is a terrible consequence to your model: all the government would need to do to strip you of all protections would be to declare that some action [perhaps the crime they are accusing you of] invalidates your citizenship.