Is it permissible for a husband to recite Surat Al-Ikhlas and Al-Mu'awwidhatayn and then wipe them over all parts of his menstruating wife's body, including the external genital area, to alleviate her pain, by analogy with the Prophet's (peace be upon him) action of reciting these and wiping them over his body every night?

The basic principle is for a person to recite upon themselves, blow into their hands, and then wipe their body with them. This is the Sunnah, and there is no difference in this between a menstruating woman and others, because the preponderant opinion is that it is permissible for menstruating and post-natal women to recite the Qur'an from memory. Therefore, there is no impediment for a menstruating wife to recite Surat Al-Ikhlas and the two Mu'awwidhat (Surat Al-Falaq and Surat An-Nas), blow into her hands, and wipe her body with them. Similarly, there is no impediment for the husband to do so and wipe her body if she is ill or incapacitated, for the Prophet, peace and blessings be upon him, used to do that before sleeping, and when he was ill, Aisha used to do that for him.