Wanted to chime in with praise for playing as Mehmed. Just finished a Monarch/Fractal game and won domination in the early 1600's!
Had Brennus very close to me and was able to take his food-rich capital and the Jewish holy city (shame it was placed so poorly, but kept it) before moving on. Normally, I would have held up a bit and plotted the total removal of Brennus, but two things made me change strategies -
1. Brennus had some cities on hills and had built Duns - a pain to take those early without siege.
2. Julius Ceaser had expanded toward me and was getting close to iron.
Didn't know if I could handle taking too many more cities, by gathered what I could (had construction at least) and threw it had the Roman capital first. In short, the war was pretty successful, and I kept more cities than I had originally planned (including the Roman Hindu Holy City). Thankfully, I had built the Oracle and took COL, and with courthouses and larger cities (thanks to Hammans and the expansive trait) I was able to maintain very well.
I took some time to retool, and was very pleasantly surprised as to how quickly my economy recovered. My continent had 5 civs (me Brennus, JC, Bismark, Alex), and the remaining two were still out there, so with domination in mind I went through Engineering and Gunpowder before trying to finish Liberalism (I was far enough ahead down that path that I figured I could detour). With Jannies, Maces, and Trebs/Cats I was able to make some inroads into Germany (after bribing Alex to take him on first) which was a World Wonder feast (should have built more troops, Bizzy). Soon, he was done and it was just Alex left to challenge - sort of.
After all of this, I retooled again for the final push. The best here is that with Gunpowder and Engineering on board, I was able to take CHEMISTRY with the discovery of Liberalism. That also allowed me to then start in on Steel for my next tech.
Here's a great stack for you: upgraded/promoted grens supported by jannies and a knight or two with trebs and then soon cannons to follow. My trouble in the past with getting grens and then cannons so quickly is that I was a fair distance from rifles at that point, and muskets had issues with enemy mounted units (usually knights, but cavs are very bad). My jannies did GREAT against Alex's knights and my stack cut through things quite well. He did get rifling toward the end of things, but I had a ton of grens so no problems there.
The other two civs (Toku and Teddy Roos) were non-factors really. One tried to make a landing and attack while the other proved to be a fairly reliable tech trading partner (can you guess which was which - you'd be right).
In all, the power of having larger cities with expansive/great UB/ combined with larger territory with Organized/cheaper courthouses was key. Match that with a handy UU that protected my grens and siege from just about anything, and there you have it.
Of course, if JC had iron early in this game, yikes!