I have yet tested this claim, but I assume if you link your account to a Facebook acc, then your game saves will be recorded by Facebook from then on. So, when you clear your game data, that means you delete your saves from Facebook, not from your device and then can you start a new one. Also, the majority of us use the signed APK, the game's code registered with our device, so we need to direct that to a Facebook acc rather than our device. If it doesn't work, try using a virtual space such as Parallel Space and install your game there or if your smartphone has a second space feature, utilize that.