Does the reward for fasting in Ramadan multiply seventyfold when going out for da'wah in the path of Allah?

Scholars have differed on the meaning of "in the way of Allah" in the hadith: "Whoever fasts a day in the way of Allah, Allah will distance his face from the Hellfire by seventy autumns," holding two opinions:

1. Obedience to Allah and sincerity towards Him: This is the view of Al-Qurtubi and Ibn Baz, meaning a fast by which the servant seeks the countenance of Allah and the Hereafter. 2. During Jihad: This is the view of Al-Nawawi, Ibn Daqiq al-Eid, and Ibn Uthaymeen, because this is the predominant usage of "in the way of Allah" in the texts of Sharia, and because fasting during jihad involves hardship.

The more probable view is that the specific virtue mentioned in the hadith applies to the one fasting while fighting the disbelievers, provided that he does not neglect a duty or fall short in jihad.

As for going out for Da'wah (inviting to Allah), it is a great good and one of the noblest acts of proximity to Allah. However, the Tablighi Jamaat's naming their outings "going out in the way of Allah" and their interpretation of scriptural texts with this specific meaning is a clear error, as texts must be understood according to the intent of the Lawgiver, not according to novel terminologies.