Flying Axe,
In my opinion you are co-mingling two different arguments.
One question might be what do Murray Rothbard and Hoppe believe is the correct response to a sane and coherent person who is able to distinguish right from wrong, who:
a. attempts murder and/or
b. succeeds at murder.
You scenario assumes that after two or three strikes your transgressor will have access to enter your private property again and again to keep harassing you. That is possible, even likely under statist laws of today but less and less likely under libertarian law..
An insane person (your non-repentant likely insane psychopathic serial killer) is a different argument altogether. The same rules of self defense and punshment theory cannot be applied without further investigation.
For instance is your attempted murderer aware of his actions or consequences or not? Is he acting with a motive or randomly? How mentally capable is he? As incapable as a squirrel that keeps chewing off electrical cords? a newborn baby who’s mother dies in childbirth? An abused seven year old that kills his father to protect his mother? Each scenario is different.
Maybe on a different thread we should discuss whether libertarian law allows you to involuntary enslave a person beyond a certan point of insanity for “his own and the public protection” This is a fascinating subject but does not fall under this discussion of libertarian law.
Was he under the influence of a drug? Was that drug self administered or prescribed by a professional? Has he had a brain injury or brain tumor?
The answer to these questions would lead you to some sort of libertarian theory on how to handle the insane or mentally impaired - which is different from how to handle mentally competent criminals.
Second part of the argument.
If a person was mentally capable but nevertheless a repeat offender- may you kill him or enslave him?
In my opinion when he attacks you the first time, you may defend yourself with force, but no more because at that stage he is not a serial offender. If you can subdue him, you may not now kill him in self defense (just because you assume he will be released to come kill you - that is a statist scenario that clouds the argument..). You hand it over to private courts, private property owners, private insurance agencies etc.
Now if he already is known to be a serial offender it is different. I know you may not enslave him just because you think he might offend (preemptive strike) but libertarian law allows you to ban him from your private property or have him sign a contractr allowing you to enslave him if he transgresses.
But if you are talking about our current statist society, they may have released him into the public domain so libertarian principles are difficult to enforce. You say to not talk about “what would ghappen in a libertarian society” but that is of paramount importance to the argument because Rothbard and Hoppe assume a certain libertarian environment for their ideas to be applied in.