Battery life estimation
The first thing you need to check is what the battery manufacturer considers to be "flat".  You may find that this is less than 1.2V.  If that's the case, you can't use the 2950mAh figure to calculate the life.

The other thing to check is that the battery is still capable of delivering 380mA when almost flat.  It's no use if the thing sits happily in standby for 3 hours, but the moment it powers up, the voltage drops below your minimum.

The better battery manufacturers will publish curves showing the expected life of the batteries at different current draws.  You would have to check those to see how long it's capable of supplying the current you need at the voltage you need.  That may turn out to be pessimistic, since batteries tend to recover when left un-used for a while.  So 380mA constantly is a lot more work for a battery than 380mA bursts.