This has some of the arguments mentioned in the question, but I touch on something else as well. Read on…
There are two reasoning's behind it, the simple one boils down to this: every person has an "unalienable" right to life, that us until such a point when another person decides to take someone else's life (without having just cause to do so, i.e. during wartime, or while in defense of oneself or one's family from peril of death or egregious bodily harm). Such a person would have demonstrated a flagrant disregard for the sanctity of life & by their willingness to kill another man & acting upon that willingness, they are deemed to have forfeited their own right to live... Such a person would be looked upon as having no respect for their own life or anyone else's therefore; they should not be allowed to live.
At this point I think Mr. Jefferson, as well as the majority of those around him, would likely view the perpetrator as having lost a good bit of their humanity, and would likely be viewed as no longer being "a person" but closer in nature to a wild beast: uncivilized, unpredictable & surely dangerous, maybe even possessed (earlier times=backwards beliefs) & that the only appropriate response for such a situation would be capital punishment. An Eye for an Eye begets a Life For A Life and all that. It makes a certain amount of sense.
Now, the second, more complicated reason...
Understand also, that a precedent needed be set, because should consequences not be appropriately meted out, there stood (in the view of the Founders, I believe) a very real danger that things could slip into Anarchy & the brand new burgeoning Republic being built could go tits up in short order. There had to be a rule of law, and Mr. Jefferson was actually being prudent, because he understood that while far away from England, the building of a Nation was underway, something bold & radical & beautiful, and very well thought out; however, not everyone could have remained rock-solid in their conviction that things would work out if they persevered. Especially when the Founders (out of necessity) took the time to lay out the groundwork & get the foundation laid. They knew it wouldn't be perfect & there would be the need to evolve with times, but it was imperative to get it as close as it could possibly get to perfect, which took time & nobody wants the drafts, they want the final manuscript/writing. There had to be disharmony & uncertainty, it's human nature especially when constructing the archetype of a nation. I know, without doubt, that it had to weigh heavy on the Founding Fathers So providing the stability & reassurance of justice would go a long way towards assuaging doubt among the weary & demonstrating to those who were less scrupulous that while they escaped Tyranny they also escaped Injustice & while some ideals were reshaped basic tenements prevail, with among them being a Fair Judicial System for those who would oppress the freedom & liberty of others.
I couldn't tell you specifically, with any one source of Emperical data anyway, how I came to this. It's a combination of what I've read & learned about Thomas Jefferson, the sense we have through history lessons about the mindset in that time, understanding of human motivations, & the willingness & ability to step back from a situation, objectively examine it from more than just a single perspective & put myself in another person's mindset. That's what I did here, and the above is the condensed, pared down to the bare bones version, cause it's been a long couple days & I'm tired; but I certainly hope it helped. Thanks for the cognitive calisthenics, OP, it was fun & enlightening!