The Bible doesn't give time limits. As I said, I understand the reasoning, but I don't agree with a total condemnation of executions. From a Christian standpoint, anything involving killing people has to be taken very seriously, because eternal souls are involved.
Okay, you've got a murderer ... he killed X people. Those people can't be brought back; they're either saved or not, based on what they believed and did before their death. However, the killer is still "pending." Is it merciful to keep him "pending"? Maybe it is; maybe he'll repent. On the other hand, maybe he will continue to harm others.
As for the rest, your logic makes no sense. You're extending to the killer a salvific exemption not extended to his victims. If we must by your logic assume that the victims have met their eternal fate because God employed the killer as the agent of His will, there's no reason not to claim the same role for the State in applying judgement; and the murderer has ample opportunity to make a full confession and perfect Act of Contrition, something of which his victims were almost certainly deprived.
There were eternal souls at stake in the Old Testament as well as the New. If the Law given by God to Moses was just and good, then the state has every right to use the death penalty AS PUNISHMENT. Why? Because it is JUST! God said so, Himself.
Who is the Pope to refute God?