Is this supplication: "O Allah, do not let my enemies gloat over my ailment, and make the Great Qur'an my medicine and my healing..." to the end, a recommended supplication for a day when the gates of heaven are open for answered prayers?

The established supplications from the Prophet, peace and blessings be upon him, should be spread and recited. It is not advisable to supplicate with what has not been reported from him, peace and blessings be upon him, because it might be permissible for an individual to supplicate with it for himself, but it should not be spread or encouraged among people.

The prophetic remembrances and supplications are the best for a Muslim to seek, and following them ensures safety and security. Anything other than them might be unlawful or disliked.

The Sharia (definition) has prohibited rhymed prose (saj') in supplication, because it contradicts humility, distracts the heart from imploring Allah, and is considered blameworthy affectation. It also goes against the guidance of the Prophet, peace and blessings be upon him, and his companions.

Examples of blameworthy rhymed prose include: "In the name of Allah, my path; and the Most Gracious, my companion; and the Most Merciful, guards me from everything that touches me," and "O Allah, O Easer of the difficult, O Softener of iron, O Fulfiller of the threat," noting that "Fulfiller of the threat" is incorrect and the correct phrase is "Fulfiller of the promise."

In summary, such supplications should not be spread, nor should people be advised to adhere to them, except for what is authentically established in the Quran and Sunnah (definition).

And the statement that the gates of heaven are open for a specific supplication is a statement against Allah without knowledge, and an assertion of the unseen, which only Allah knows. Allah has warned against this.