Not an Alternative world, but a reason to go out and research. While reading
The Arabian Nights: A Companion I found out two things that would make good adventure hooks.
First, the French translation of the Arabian Nights, which was the first into any european language, was a translation of a manuscript in four volumes, one of which is missing! Just think of the crosstime adventures looking for that missing volume or the older text from which it was copyed. And the
Arabian Nights is hardly the only such text to look for.
Second, the Arabian Nights wasn't originally written either in Classical or Modern Arabic. It's from Middle Arabic. There is no diffinitive dictionary of Middle Arabic! Compiling such a dictionary could lead the PCs through many alternative Arabias. some wilder than any in Scheherazade told of.