Of course IST is a much smaller airport. However, domestic-to-international could take time. It's two separate terminals -- you generally have to get from the domestic terminal to the international terminal via a walkway, then go through security and passport control at the international terminal. International-to-international at FRA could be quick, or not; you never know.

P.S. TK flies non-stop ESB to FRA and DUS, and LH flies ESB to MUC. Perhaps you could make one of those work.

P.P.S. 1:00 am to 4:00am is peak time at DXB. I understand that you might be bleary-eyed, but there will be plenty of activity at the airport to perk you up, and at least you are going less out of the way and getting a significantly shorter flight to CPT.