How to Delete All Cached App Data for Testing APK

I've been pulling my hair out trying to finalize testing on an Android app that will not release data from the previously installed version. I'm using a Nexus 7 and Samsung Galaxy, and no matter what I do — clear the app cache, clear the app data, force quit the app, uninstall the app — it continues to load the new version with the old problems in place, and I know they've been corrected. The way I know this is that I did a complete wipe and factory reset of the Nexus, used a new Gmail account specifically for this experiment, and the app loaded as it should. But once I go back and try my admin Gmail account, it goes back to loading old data again.

Is there a way to COMPLETELY delete old data, so that each test of the APK is as if it was by a first time user? The Beta Test area I'm using in Google Play is no help.

Thanks.