I made a simple web app that will let you change the game parameters of a save file, including the turn mode: Civilization V save editorCivilization V save editor
Just open your save file in the app and change the value under Turn mode. Then download the new save file with the changes and open it in the game.
The only other alternative I'm aware of would be to edit the save file by hand. This is the source I used for adding the functionality to my web app: http://blog.frank-mich.com/civilization-v-how-to-change-turn-type-of-a-started-game/