The 2nd Amendment Argument and Methodology to deter crazies from going around shooting people can be corrected easily.
The simple answer is: Leave the 2nd Amendment in place as is. Leave the the laws in place that say insane people cannot possess a gun. What must be changed is those who wish to own guns must prove to the State they are sane, not a harm to themselves or others. Proof must be presented before a purchase of gun can be made. Test via Psychiatric professionals must be paid for by the person desiring to purchase a gun.
Those wanting to purchase a gun might be interested in this link, here.