I believe the entire debate centers on the fact that you should not touch The Qur’an in a state of impurity, but I think the idea that menstruation=impurity is far-fetched, because you do not need to be in a state of Wudu in order to touch The Qur’an, you just need clean hands. 

Even Sheikh Uthmayneen would make the argument that those (like you) who are memorizing The Qur’an are allowed to touch The Qur’an, and they make these odd “exceptions” if it is not just The Qur’an, but if it has a cover, or if it has tafseer, or English (or some other) translation in it. I find these cumbersome. 

The Hadith that I know are the following:

In Sahih Muslim, narrated by Abu Huraira:

“While the Messenger of God (may peace be upon him) was in the mosque, he said: O ‘A’isha, get me that garment. She said: I am menstruating. Upon this he remarked: Your menstruation is not in your hand, and she, therefore, got him that.” 

Other variations, I believe (not sure) have Aisha actually touching The Qur’an. But, other than that, there is nothing involving that. 

Furthermore, we have this:

In Bukhari, narrated by Aisha:

“The Prophet used to lean on my lap and recite Qur’an while I was in menses.”

The Prophet is touching Aisha, who is menses, and reciting The Qur’an, and while The Prophet was illiterate, it becomes clear that menses itself is not the problem, especially when we consider that The Prophet would allow his wives to comb his hair, to share food, and a whole host of other activities. 

Furthermore, a woman is allowed in the Mosque during menses, and thus able to touch things in the Mosque, which makes this stance of women being unable to touch a Qur’an while in menses to be rather odd, since the concern, again is about the cleanliness of one’s hands. 

I will try to find other examples, but those are the ones that I remembered, and insha Allah, if you find anything else, please send it over to me. 

I hope this helps in some small way, insha Allah.

-Osama

For anyone who was wondering. Here you have it.