Is it possible for the intention of a full recitation of the Quran (khatmah) to be for each part with a specific intention, or for all parts with a single intention?

Sealing the Qur’an does not require an intention, because its recitation is among the matters that are only acts of worship, so intention is not a condition for it. Therefore, the intention to seal the Qur’an is not stipulated at the beginning of the recitation nor at its end.