All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
It is prohibited for a menstruating woman to recite Quran even from memory. The proof of this is what was narrated by Omar Ibn Al-Khattab, Ali Ibn AbiTalib, Jaber Ibn Abdullah and Abdullah Ibn Omar (May Allah be pleased with them all) and this view was adopted by Shafiee, Hanafiee and Hanbali schools of thought, in addition to one narration of the Maliki's. Ali Ibn Abi Talib narrated: "Nothing prevented him (PBUH); or the narrator said: Nothing prevented him from (reciting) the Qur'an except sexual defilement. Al-Tirmithi graded it as Hasan Sahih and Al-Hafed Ibn Hajer graded it as Hassan in the book [Fatih Al-Bary vol.1/pp.487].
In addition, Janabeh (Major ritual impurity) and menstruation take the same ruling since both are major impurities. As for forgetting verses of the Holy Quran, this is not a sound excuse since you (Questioner) could have listened to recorded verses and the like, revised them after the menstruation period is over and pondered over the meaning without uttering the verses. And Allah Knows Best.