Gustavus Adolphus
Have something happen to remove Enver Pasha from power as by some accounts he virtually dragged the empire into the war on his own. Both accepting the German offer of the Goeben and then agreeing to it's attack on the Russians in the Black Sea.
Possibly have someone suggest to the Ottomans that they can seize the Goeben if it doesn't leave port shortly. If it does then it's pretty much doomed so the Ottomans could probably pick it up, with total control rather than being a rogue with a German crew.
Churchill was a pretty poor diplomat but the complaint about Britain taking over the ships being built for the Ottomans is just propaganda. Very doubtful if any other country in Britain's position would have done anything different. It was more Enver and other's who wanted to go to war on the German side used it as an excuse for being anti-allied.
This is still more likely to led to a neutral Ottoman rather than one on the Allied side but you can then have some German diplomatic blunder, or allied success making it look like their going to win and the Ottomans commit.
Steve