Hi Timbo,
Another thing that would probably keep the LEDs consistent would be to add a 1000uF/16V capacitor across the power supply (battery).
Pulse-Width-Modulation is used to efficiently vary the brightness of lights, the speed of motors and the temp of heaters. Your home light dimmers and my Plants circuit use it, and so does our variable-speed drills and furnaces.
Instead of using a huge, hot (wasteful) variable reostat in series to vary the current, PWM uses a transistor, FET, SCR or Triac as an on-off switch. Since it is either fully on or off, it barely gets warm. It is turned on and off pulsing very quickly so you can't see flickering nor feel vibration. If you want the light to be bright, the motor to be fast and the heater to be hot then have the on part of the pulses the widest. If you want a bit of dimming, the motor slowed or the heater cooled a bit, then reduce the on time of the pulse and increase the off time. If you want the light to be very dim, the motor very slow or the heater just warm, then reduce the on time of the pulse to near minimum and increase the off time to near maximum.