Thanks for your response, JayJ.
I did a bit of online searching and found Helium (formerly Carbon). I completed one level of my game, and then backed it up using Helium. I then uninstalled the app. Using Helium, I restored the app to my N7 and lo and behold there was the full completed first level!
It's my fault for not doing a test run like this on both AirDroid and My Backup Pro. Both have been uninstalled from my N7 as they are fairly worthless, at least to me. Helium is now my new backup for app data -- because it works.
But, yeah, a drag to have lost all that data, even though I was doing what I thought was the correct/right thing to do.