Constancius,
Since you posted this here on Research and Authencity I'm imagining that you don't want just a pat-on-the-back "that'd look nice" reply.
1100-1300 is not the transitional armour period, although there are similar armours in the period you mention. Generally speaking, I think of "transitional" armour as the period where maille gradually is augmented or replaced by plate in most of Western Europe, and can be roughly defined as "the 14th century" or 1301-1400. That's a very broad statement, and you will find other opinions and exceptions.
I have read that it wasn't uncommon in the 1100-1300 period you chose for European knights or groups of them to "hire out" to Saracen local leaders or cities, but I've never seen a reference of them using other than the clothing, arms and armour common to their own origin. Please bear in mind that I'm just a hobbiest with an interest, and by no means a historian.
More tersely, I wouldn't do it. There's a standing joke in some SCA communities about "Abu MacGregor, Sheik of the Heather", and you're just about to put yourself in his shoes.
If it's what you want, then I'd just do it and not worry about a foundation in history. If you represent it as a fun personal choice and don't present it as historical, then you have nothing to defend.

Bob