Default Combining APK + data into new APK?


I'm trying to figure out if there is a way to convert a APK plus its data into a single new APK. The specific example is: I have downloaded and configured Authenticator for a number of accounts, and I'd like to back up both Authenticator and account data into a new installable APK.

Before you say "Titanium Backup" - note: I cannot install Titanium Backup onto the device as I cannot root the device, and the TiBkp backup file created by TiBa is NOT an installable APK.

Any suggestions?