How about tiltable mirrors ?
As soon as the sun gets up in the morning, a high illumination level is available immediately. In the evening, nearly full illumination levels are available until the sun sets. At noon, the mirrors could even be used as shields against the hot sun :-).
Thus, the solar power would only be required to turn the mirrors during the day, instead of illuminating the chickens.
Do you have any information, which wavelength would best stimulate egg laying ? If in the yellow band, low pressure sodium could be used to extend the light period, if in the blue range, blue LEDs would be the most economical way.