Another mod thing to help the Turks is to give them armour.

In vanilla (unmodded) MTW the Turks usually defeat the Byz.

Like Gollum, I have never seen them make JI in years of play regardless. My impression is that the AI has it's own agenda for the factions depending on which one you choose to start with. I've never been able to successfully help someone survive who is going under - they end up doing things like leaving territories undefended. So your best bet may be to mod the Turks and start as England, as someone suggested.

Taking the Eggy sultan works for the Turks on early in vanilla MTW, where the sultan starts in Antioch. You have to take Tripoli from Syria with everything you've got on the first turn. Sometimes you'll get him twice if he's repatriated to Arabia, and you can take him again. Usually then the Sinai goes rebel, so the Eggy's are down to one province, Egypt, with a rebel buffer. You can go neutral with Egypt then, or march on in. The big trick with this strategy is keeping the loyalty of your and the newly captured territories. Further on, if you don't want conflict with the Almohads then don't send any ships along the North African coast - just cover off Egypt in the gulf of the Nile, and trade with the north Med.

I'm curious about why you don't try playing the Turks ...