Here is another "solution":
- don't waste time on this issue.
because:
- you don't expose a public interface to the world, so you are free to change your webservice interface at any time via update of webservice and an update to your app.
- the app is "very trivial" (as you called it) and probably isn't used much at the moment
- you probably have better things to do right now and are just consuming time
if there are suspicious performance or query spikes go for the least time consuming solution:
- introduce a password (clientid) saved in your app (blocks 95% of these users) this clientid can later be used to identify different clients if other programmers want to legally access your service
- introduce rate limiting (as mentioned above)
this will in 99,99% solve your problems and you can get to work right now and write awesome new features.