[e.k.]

A great improvement with hopefully little implementation effort would be changing the default name of the backup file:
Currently it is always MobileSheets_yyyy-mm-dd.msp
It would be really convenient to set it to <library name>_yyyy-mm-dd.msp instead.
The backup file name for mobilesheets.db would stay MobileSheets_yyyy-mm-dd.msp or become mobilesheets_yyyy-mm-dd.msp - fully consistent, no change of the current behaviour.
The proposed backup file name for e.g. msptest.db would be msptest_yyyy-mm-dd.msp or MSPTest_yyyy-mm-dd.msp. The capitalized name could be taken from the library name that has been specified during creation of the database and is displayed in the "Switch Library" window.

I was fallen into the trap with different librarys and "just" backup file name "MobileSheets_yyyy_mm_dd". 
I would give a +1 from my side to itsme´s suggestions.

e.k.