In the Navigator/Parameters/Translation you can set to default projection engine. But even if you don't, FME is specially good at reading in a tree of sources, applying a projection and writing them out again to a new tree with exactly the same tree and names. Read in everything with one reader using a wildcard and folders, set the writer to Dynamic and the new projection name and press Go. It will do each one but how is not your problem! The largest set of files I have loaded is 20,000 csv files from a Lidar dump. Fast and easy.