Not too much work on your part, it would seem to me. Basically, the main areas to translate would be feats that reference unique True20 mechanics (there aren't too many of them), powers (some of these are D&D spells like Dispel, Find the Path, or True Seeing, but others are fairly unique), the new uses for Conviction (easy if you're using action points), and the various antagonist/ally stat blocks. Most of the book is about story, the *feel*, language, and setting of the Nights, so it's useful as is.
Glad to hear it won't be too difficult. There are a few specific things in particular that I'm interested in:
I've always wanted genies that were closer to those described in the Arabian Nights than the ones that exist currently in dnd. Would it be possible to adapt the stats in your product for the different types of djinn into a standard d20 game? If so, are the rules for summoning djinn also adaptable?
In the stories of the Nights storytelling is more than recreation, telling a good story can often save a character's life or have some other major affect on events. You did mention there were storytelling mechanics and those really interest me, but they sound as if they rely on a lot of True20-specific rules. Is any of that stuff adaptable to regular dnd? Could I conceivably have a standard d20 character (using relevant mechanics adapted from True20) launch into a story which would then play out using True20 rules?
This doesn't relate to the d20 conversion issue but I'm curious; are Sufi mystics or Peri (which I realize are more Iranian than Arabian) present in Caliphate Nights?