... there might be a collision there ... perhaps wake up periodically ... make sure the app isn't currently running ...
I think that you are getting far too complicated here. The file system isn't going to corrupt files by reading and writing them at the same time. We know that a 100% up-to-date backup is not required because at present there is no backup at all. Having a service that wakes up periodically is going to be difficult to write and even more difficult to test with 100% confidence. I would go for a simpler solution.
You don't say whether your app has dozens or hundreds of files, or whether the files are hundreds of bytes or kilobytes long, or whether the files are updated with human-keyed text or some computation cycle, but here is what I would do. Associate each file with a flag (integer), preferably in an object, and make a list of these objects. The normal value of the flag is zero. When a file is saved locally (ie updated) its associated flag is set to one. A timer looks through the list of flags every ten seconds (or every ten minutes, if you prefer). If it sees a flag set at one it changes it to two. If it sees a flag set at two it knows that the file has been updated locally, but not that recently (not in the last time cycle, or the flag would have been reset to one), so it backs it up now and resets the flag to zero.
It seems to me that this would be a very rugged solution. The timer procedure overhead would be very small - less than the time taken to enter a text character, probably - and would normally result in no backup action anyway. If files are being updated by user action then the backup would be deferred until the user goes quiet. Very important (to my mind) is that it would be quite easy to test.
[Edit : I forgot when I wrote the above yesterday that your app only updates files locally during (Pause), but I decided that that would not change my suggestion. I think that if you want to offer a sensible cloud backup function then you should write both to the device and the cloud regularly. Two other factors that you need to prepare for : there might not always be a reliable internet connection available, and 'phones get turned off sometimes.]