If you'll bear with me, I'd like to address the question by first considering the conditions for forgiveness. The relevance will very quickly become apparent.
▻ CONDITIONS FOR FORGIVENESS
When forgiveness is granted or recognised as appropriate there are usually three conditions in place :
1) Wrongful (and so avoidable) harm is caused by one person to another, with that act recognized as harmful and wrong by each; 2) the person who caused the harm (a) acknowledges responsibility for it, (b) expresses regret and (tacitly or explicitly) offers assurance about future conduct, and (c) either through the combination of (a) and (b) or in addition to them, asks the person harmed to forgive him; and (3) the person harmed assents to the request - that is forgives - implying with this that the original act has in some sense been nullified or repaired. (Berel Lang, 'Forgiveness', American Philosophical Quarterly, Vol. 31, No. 2 (Apr., 1994), pp. 105-6.)
▻ YOUR THESIS DISTINGUISHED FROM THESE CONDITIONS
The language is a bit dense but these conditions seem plausible. In terms of this schema we can now define your position or what I take to be your position.
Which is :
THESIS. Whatever wrongful (and so avoidable) harm is caused by one person to another (whether as crime or moral offence or both), the penalty of death should never be imposed.
This means that you drop conditions 2) and 3) and part of 1), namely 'with that act recognized as harmful and wrong by each'. The offender may not recognise their act as harmful and wrong.
I'm not preparing for a criticism, far from it. I just want to get your position into clear focus. I hope I've got it right. (For myself I cannot imagine conditions in which I would apply the penalty of death whatever the crime or moral offence. Offenders may need to be removed from positions of power and be confined so that the public is safe from them. I've no objection to that.)
But this is not the place for opinionising. Argument is needed, and it is precisely what you are looking for.
▻ ARGUMENT FOR THESIS : THE PERMANENT POSSIBILITY OF REDEMPTION
The language of 'redemption' is often associated with religion but the argument to be offered has no such association. An atheist or an agnostic can accept (or of course reject) it.
It is always possible that the legal or moral offender will (to borrow from the conditions set out at the start) :
(a) come to recognize their act as harmful and wrong
(b) come to acknowledge their responsibility for it
(c) come to expresses regret and (tacitly or explicitly) offer reliable assurance about future conduct
If conditions (a) to (c) are met, is a world in which an offender redeems him- or herself not preferable to one in which an offender merely ceases to exist because put to death ?
But suppose we know that someone will never reform, will never redeem themselves? The argument does not work for this kind of case. My answer is simple and twofold :
(i.) No such knowledge is humanly possible.
(ii.) The rule of recognising the permanent possibility of redemption has sufficient intrinsic moral merit to justify it even there are some cases it fails to justify. Likewise, there is intrinsic moral merit in the rule against gratuitous lying even though in some cases such lying might have good consequences.
Joseph Beatty, ''Forgiveness', American Philosophical Quarterly, Vol. 7, No. 3 (Jul., 1970), pp. 246-252.
Berel Lang, 'Forgiveness', American Philosophical Quarterly, Vol. 31, No. 2 (Apr., 1994), pp. 105-117.
Arnold S. Kaufman, 'The Reform Theory of Punishment', Ethics, Vol. 71, No. 1 (Oct., 1960), pp. 49-53.
Herbert Morris, 'A Paternalistic Theory of Punishment', American Philosophical Quarterly, Vol. 18, No. 4 (Oct., 1981), pp. 263-271