Rollo,

Another alternative might be to try tying a turban/puggree around a tarbush or central cap (as, for instance used by the mamelukes), this is a cap, either truncated conical (like a fez) or cylindrical (akin to a tall and stiffened chittral cap) which was worn fairly centrally on the head with the pugree or turban wrapped or folded around the base (usually twisted front and rear to give raised sides) (The idea of the pugree still exists in the West in the wrappings about pith helmets).

I'm unsure of the dating of this practice in civilian headgear, but there are certainly Persian and Indian prints from the 12/13th C AD, shewing the pugree worn around helmets and the practice seems to have been somewhat older.

Regards

Walrus