Can logic be irrational?
Maybe he just wanted them to be together, and he couldn't carry all of her so took the most important and portable part?
In a sense. Logic is simply the construction of linguistics in such a way that statements made with it are internally consistent, and as such, sound.
What's rational on the other hand, is what logically follows from a set of values.
For example, what's rational to a person who wants to die, is not rational to a person who wants to live and vice versa, but it's possible for both of them to have logically sound arguments for how to pursue either goal granted that we accept their core values.
Sephiroth might be mistaken in his view about his background and his relationship to Jenova - but his logic might be sound and could make rational sense if he was right.
Whether he's right or not however, isn't a matter of logic, or reason - it's a matter of empirical inquiry which is something else entirely.
As for why Sephiroth took the head -
Because he couldn't bring all of her, and since, as I've gathered, Jenova isn't actually a person, but a virus/parasite of sorts, it doesn't really matter what part of it you take as long as its infected with the cells.
The human-shaped thing is, as far as I understood, just a human(or ancient) host that hosts "Jenova".
And with that being said, looking at the shape of the host in the glass, it doesn't seem like there are many other parts that would be easy to cut off and bring along.
As for buster sword not splitting Sephiroth in half - I am pretty sure it doesn't mean anything at all.
It's just a result of devs and writers not really giving a damn "becuz vidya gamez".
Writers go -
"Cloud back-stabs Sephiroth and mortally wounds him, unfortunately you (designers) gave Cloud a ridiculously broad sword, but hey, we also have battles were machine-guns do damage that's next to inconsequential, so whatever right? It still looks kinda awesome if nothing else."
Sakaguchi goes *thumbs up* and that's it.