Unable to sync saved data for Minecraft, and don't want to loose newer unsync'd worlds

I have a bunch of old worlds from the 360 and Xbox one, and a while ago I would get an error message telling me that I could not sync data because I was out of space. Foolishly, I ignored this warning and continued to play the game. Now I have a world that me and a couple of friends of mine play that I really don't want to loose, but I'm afraid if I clear the local data to make more room (which has been the only method to fix it I've seen while trying to figure this out) it might delete my newer worlds. Is there any way to fix this? Or do I need to get a storage device or something.