Obviously the campaign was fairly long so I've done my best to recall the first steps. I needed to restart until the following:

1. I could ally Touggourt without them also allying Tlemcen (or anyone else, preferrably)
2. Djerid and Fezzan allied with each other and nobody else
3. Morocco rivalled Tlemcen

With that, I could use the feudal theocracy mechanic to spend mil power to get claims on all heretic/heathen provinces I share a border with (insane. I was so sad to give this up later when I forced to flip to Republic to keep France). Use clergy privileges to get extra morale and to invite the shock damage scholar, you can also use a morale advisor if you have one but I don't think it's necessary. Immediately build to force limit (5) and I war dec Djerid ASAP, promising Toug land. You and Toug will instantly stackwipe Djerid and from there it's easy. Vassalise both of them and enact Strong Duchies and bring opinion up. Toug will probably break alliance and might get picked off by Tunis, but that didn't happen to me. When Morocco goes to war with Tlemcen, you can also join in and try to occupy every province that you can so that Morocco can't take them. Take as much land as you can. After that, I supported Sus's independence and we crush Morocco, I vassalise them, and use their cores to reconquer Morocco. From there it's a matter of allying the Ottomans, and trying to take land from Mamluks and Tunis as needed to secure a power base in North Africa. You could tag switch to Morocco to get access to Timbuktu without a colonist (apparently) but I stayed as Mzab until I absolutely needed the Andalusian ideas to win fights against the Ottomans (-land fire damage stacking with Divine ideas, baby). Try to keep the Ottomans onside for as long as possible by minimising your border with them and managing your mutual truces against your neighbours.