Hi,
You sounds interesting. I would suggest to add a uP to PWM the LEDs. The leds consume quite some energy, but our eye can't understand if they are flickering in high frequency (look at TVs/Screens).
By placing a uP, you can have the LEDs blinking 64 times per seconds at max bright, at 1KHz. You would save 93% of energy :)
The uP itself can be chosen and programmed to use utra low power. Consuming even less than the LEDs.
I understand there is no on/off switch? It can be easily added.
Depending on the energy you would like to store while the peltier is connected, the caps are to be dimensioned.
Filipe