Will [1] Honest Ibe Hooper or [2] Boy Reza Aslan or some other giant of Moderate Islam denounce the Jama'at al-Tawhid wa'l-Jihad as Misunderstanders of Islam or even as Greasy Islamophobes? Or are they not misusing the Qur'an and Muhammad's words at all?

"Gaza-Based Salafi Group Launched Rockets at Israel," by Chana Ya'ar for [3] Israel National News, August 28 (thanks to Benedict):

A radical Salafi Islamist group affiliated with the international Al Qaeda terrorist organization has taken responsibility for launching Sunday morning's Grad rocket attack at southern Israel.

The Jama'at al-Tawhid wa'l-Jihad (JTJ) jihadist organization (Group of Monotheism and Jihad) allegedly issued a statement claiming “credit” for the attack on Be'er Sheva, the largest city in Israel's southern region. [...]

Among the Koranic texts taught by al-Shami and cited by JTJ in justifying its slaughter is an alleged quote from the Islamic prophet Muhammad, “Whoever slaughters a non-Muslim [at war with Islam, or 'enemy occupiers'] sincerely for the sake of Allah, Allah will make hellfire prohibited upon him.”

That's not in a "Koranic text" at all. That's a hadith.

Another quote allegedly from Allah (G-d) often cited by the group to justify its actions directs operatives to behead its victims: “When your Lord revealed to the angels: I am with you, therefore make firm those who believe. I will cast terror into the hearts of those who disbelieve. Therefore strike off their heads and strike off the fingertip of them.”

That's a Koranic text: 8:12.