I think that I might have eased the Deli/Djeli irregular cavalry problem for myself at least, using older Baccus cossacks.  I was given an unpainted Russian Napoleonic army a few years ago. (The army had been in the previous owner's painting queue for years.)  It had a couple of units of cossacks that I didn't paint at the time, because there were more than I needed.  They have taller hats than the current ones, presumably modelled on tall fur hats.

For Yoruks (Tatars) I am intending to get some "NRU33 - Tartar Cavalry" from the Napoleonic Russian range when I can do my next order.  I have a feeling that when the Russians grabbed some of the territory that housed Tatars, the Ottoman Empire rehomed quite a few in what is now eastern Bulgaria and Rumania, but then was part of "Turkey in Europe".  Might get some Arab cavalry at some point, but I have an order in the pipeline and nearly £50s of stuff to get for the order after that that I can't place yet.

https://www.deviantart.com/donkuchi/art/Untitled-808261227

I used 18th Century Ottomans for my army.  I used Pancerni, Janissaries, and Levant Infantry, as well as levant artillery