Low voltage and high current is the perfect recipe for lots of losses.
I see plenty of steel springs (high resistance) and other crappy materials in those adapters. AAA cells, if alkalines, have quite high internal resistance. Trying to overcome this may be a waste of time, in my opinion. Clean the contacts with some alcohol, and move on.
LEDs exhibit exponential class voltage/current curves, this means slight variations in the voltage they are fed (Vf) with can drastically affect the system's current flow as long as there's no power source bottleneck.
This means the led's resistance to current flow decreases with increased voltage, and also with temperature!
Led's forward voltage (Vf) care/tuning is the role of the driver (or a cheap current limiting resistor if such a simple approach is enough for our needs). 
Cheers ^:)