RE: Prop Selection and battery life
First things first... I have zero experience to offer, just thoughts about how I might consider resolving this issue...
In calculating the volume of air pulled per revolution between a 19x12 and a 20x11, the 20x11 actually pulls about 1.5% more volume. Take this and couple it with the additional mass and length of the prop, I would say if everything else remains a constant, I would anticipate it pulling more energy from the battery.
Going to a 20x10 would pull only 92.33% of the volume of air that a 19x12 would... Which I would believe will be a better solution than a 20x11.
However, all things will not remain a constant... The plane would fly slower and thus less energy required due to the drag co-efficients... Gets into physics I don't understand...
Experiment with a couple different prop combinations... I would think a lower pitch prop will provide for more torque...But that may result in pulling more energy from the battery for your flying style...Too many variables to deal with for me...I would recommendgetting a couple of different props and go with the one that fits the needs and your style of flying...
Food for thought...