Does the responsibility of the memorizer of the Qur’an, as well as his punishment and reward with Allah, differ from that of someone who is not a memorizer, such that it yields a double-edged outcome of either Paradise or Hell?

Engaging with the Quran is among the best deeds, and the hafiz (memorizer) of the Quran who acts upon it holds a great status with Allah, as stated in the hadith: "The one who is proficient in the Quran will be with the noble and righteous scribes (angels)." His rank is higher than one who has not memorized it. However, memorizing the Quran does not entail greater religious obligations or the prohibition of permissible matters, for Muslims are equal in their religious obligations. The Quran is either an argument for you if you act upon it, or an argument against you if you do not.