I agree about Gun Free Zones needing to go.
However, unless we curtail the rights of people to appeal - drastically - then the cost of 3 meals and a cot for lifetime don't come close to the cost of legal fees in a death penalty case. So, arguing costs in favor of the death penalty only work (as would your proposed timeline) if we gutted the appellate system.
If we did that, then what would happen to other sorts of appeals? Would we limit restrictions on appeals to capital cases, only? Or would we put severe restrictions on all appeals? I don't know about you, but I really, really do not like that idea at all.
Quite frankly, I don't think life imprisonment is exactly a cakewalk. It costs less than the court cases typically associated with dealth penalty trial and appeal; it allows an opportunity to mitigate the harm to the convicted, should exculpatory evidence turn up at a later time.
So, I don't favor the death penalty in general, and I really would not support it if the appeals system were gutted.
Note that this has nothing to do with thinking the life of the criminal is sacred, in my case. It just has a lot more to do with human fallibility, and my unwillingness to be part of a system that railroads people.