IMHO the Alexandretta option would have been much better (and much more successful) than the blood bath at Gallipoli; the impact would have been very significant, cutting the empire in two, and threatening to move into either the Anatolia proper or toward Damascus.
I would not have tried to force my way through the Cilician gates, however; and the idea of pushing toward the Caucasus is quite ambitious, but might become a logistical nightmare. Possibly the best option might be to push along the cosast, and, as soon as the front stabilizes, threaten it from the back with another amphibious landing. I would think that the Ottomans would have significant difficulties in opposing such a strategy, given the total domination of the Egean sea by the Entente; and logistic issues would be deal with much more easily.
My guess: OE pulls out from the war before winter 1915; under such an assumption, the peace treaty might be much less punitive (it's not in British interest to create a vacuum in the region which might be exploited by the Russians: the friends of today....): the economic interests of UK and France might be better served by a tightening of the Capitulations regime; possible exceptions might be Palestine and Lebanon (not so much as a naked land grab, but rather to toss a bone to the French whose stewardship of the Holy Sites would become much stronger); the straits would be garrisoned by Entente troops, obviously.
Outcome: Russia can be fed through the straits (and even more importantly can export though the same); a new front can be opened in Western Thrace, knocking out Bulgaria - if they still get into the war - and creating a supply route for Serbia. AH position should get worse very very soon (at best, I give them until the death of Franz Joseph). How long do you think Germany can last in such a scenario?
It would be a negotiated peace for Germany and OE; A-H would be partitioned. It might be hoped that the 1917 Versailles treaty would be less punitive than the OTL one, but I am not really convinced of that. Best outcome for Germany might be loosing all the colonies and Alsace-Lorraine (assuming tha Russia is satisfied with some minor gains in the Caucasus and Galicia)