Well in my opinion bowmen or arquebusiers seems the next natural unit.
It seems you really have in mind what you want,
I could share a little dossier with some crazy ideas of what I could see interesting for an araby army (click to enlarge)
- Exhalted saint people: faquirs, serpent tamers, spit firers, ultra thin saints, and exceptional people.

- Dervisches

- Swordsman and hand weapon soldiers

- Harem guard:

- Thieves band (40 men) with his leader Ali baba

- Elephants and huge monstruos mounts.

- Assasins hashasins sect and haschis consumers

- Astrologer and alchemist. They can summon elements (fire, stone, wind, water) so elemental daemons/djins sounds perfect. Also they can read the stars.

- Desert nomads and camels.

- Pirates of the east sea and barbary pirate. Barbaroja and Simbad journeys

- Cannons (turks were famous for their cannons... big big cannons). They were obsessed with the thick walls of constantinopla... 700 hundread years willing to torn away those walls.

- Horse archers with Phartian shot.

- Heavy armoured kataprhakts as sassanid.

- Subjugated tribes, people from the distant corner of the vast empire, as indian or kushite black people.

- Archangels and winged soldiers. Despite they were iconoclast they have a strong tradition of angles.
- Djinn or magic spirit of the desert.

- Giant Worm riders tribe from the sandland.

- Guards of palace: two handed alphanx

- Sultan and cohort

- Summoned daemons

- centaurs from the desert

-Kapiculu or slaves of the gate, the guards of the sultan

- A unit of sandorcs. They use to ambush and assault caravans in the desert. Also act as mercernaries for the araby army in times of war. When they are hired in the arbay army they have the stats of Guards.
This units are spearmen + elite (+1atack) + unrealiable (-1comand)

Unit: Guards from the Harem of the Mighty Sultan Mustafá al Gadafi,
The idea pops remembering the guard of the libian dictator, a bunch of fatal and beautiful women holding maching guns.
Guards from the Harem are highly skilled slaves trainned to make love to the sultan and war to the rest of the men. The leader of this regiment is Dalaila, a empire born from Tilean who was kidnapped by arabs pirates while whe was a children. Now an assasin of exceptional beauty is the most loyal follower of the Sultan.
When things goes bad for Mighty Sltan Mustafá al Gadafi in the battle, he join this unit of camel raiders and launches himself to the heat of the war.
This unit is camel raider + banner of defence
