I made a simple web app that will let you change the game parameters of a save file, including the turn mode: https://bmaupin.github.io/react-civ5save-editor/

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/