This is what you need to do...
Use GC to load your first base to the original app. Clone the original app.
Use 2nd GC and load second base to the original app. Clone the Original app again and name it something different than the first clone.
Use the 3rd GC to load the 3rd base to the Original app.
This should allow you to run all three bases on the same device without having to switch GC Accounts.
I have tried this and it works.
Edit:
The cloned apps still will not be able to sync with GC, but you will have your bases loaded in them.
EDIT 2:
Use iBackupBot (nonjailbreak) or iFile (jailbreak) to clone the applications yourself. Alternately, you could figure out what files contain your base, copy them from the original app to the clone, change GC, and repeat.