Everything quoted is true with one exception.
But one must also recognize that there is a weighty tradition to the contrary and that a large number of Muslims, possibly the majority, does not favor these reformulations."
Jihad is something that Islam can't really live down, but most people of any stripe are not interested in engaging in holy war. The problem is Wahhabism, which was originated by the House of Saud. It is still actively promoted by them and they want it to be the default sect of Islam. Wahhabism teaches that jihad is a duty of all Muslims in the same sense that praying five times a day and making a pilgrimage to Mecca is a duty. That would be the reason why 15/19 of the September 11th attackers were from Saudi Arabia. Al Queda is Wahhabist, and so is the Islamic State.
I hear Trump went to Saudi Arabia to kiss ass a couple weeks ago. Isn't interesting that at this height of anti-Islamic sentiment, our leaders are embracing the Saudis? Funny how this idea of Wahhabism has had zero press since 9/11 too.
By the way, if you want a real introduction to Islamic history, pick up a book called 'Destiny Disrupted'. I am the mushy liberal who welcomes all -law abiding- muslims, but I recommend the book in the sense of 'know your enemy'. It's not a book to change anyone's opinions. It may give you some perspective on exactly how far the Islamic world has fallen. It will refine your priorities of what sects to keep an eye on.
Honestly, Islam is a hell of a lot more problematic for its practitioners than to anyone else. The religion is fucked, and more or less incompatible with either the modern concept of the nation-state and generally prohibitive of democracy. But western civilizations beat the Islamic world so badly in the 18th and 19th centuries that we don't even bother to teach that part of history. The entire history of the Islamic world does not even merit a footnote in most western histories. And if you'll take a look at (e.g.) the civil war going on in Afghanistan, it will hopefully become clear that these people are mostly dangerous to themselves (especially in the sense that sharia law does not apply to non-Muslims). However, to the degree that there is a threat, let's do be specific about which country is exporting terrorism and terrorist ideas.