Isn't the Prophet's dedication of the last part of the night to visiting Al-Baqi', and his repetition of this during 'Aishah's nights, evidence for the permissibility of specifying a time for visiting graves, contrary to what you mentioned in Fatwa No. 32569?

Visiting graves is permissible at all times, and there is no evidence to suggest that it is particularly recommended during the last third of the night or on specific days. The Prophet, peace and blessings be upon him, visited Al-Baqi' during the day and at night, both individually and with groups. Scholars have not mentioned any special virtue for visiting graves at night; rather, some have said that it is preferable to visit them during the day due to the eeriness of the night, unless one finds comfort in God, in which case there is no difference for them between night and day.