Try this idea, remove
Al-Ghazali from history. Simply have him die young or otherwise fail to be an influential author. Al-Ghazali's utter hatred of secular thought has marred Arabic culture for centuries.
In this world, Islam doesn't get to the industrial revolution first, they lacked key resources in the right areas, much like China. However, when the changes come, there is less resistance to them. The Printing Press is adopted in 1500. When solar energy devices are shown in Paris in the late 1700's (as they were in our history) the Arabs would have pounced on the technology and worked to develop it. Instead of a huge gap between the West and Islam, it would be more of a continuum.
Think of a 19th century were the Ottoman Empire was still a serious threat to Europe. I could see a big war in Europe just after 1815 because the Ottomans see an exhausted Europe as an easy target. Just picture the refugees in America. This could spin so many ways.
The Corsairs don't seem to have been ignorant of the Americas, but it seemed to be beyond their imaginations to think of going across the Atlantic. A 17th century with Morrocan pirates in the mix would be very different. Picture a Corsair republic on the Spanish main. You could blend the themes of the Reconquista with slave revolts.
The 20th-century wars become vastly more complex if the Arab lands are at least as developed as Bulgaria or Spain. Having new fascist powers on the southern side of the Mediterranian makes for a much darker WWII.